How old do we think the characters are?

I’ve just finished watching the end of the drama and I noticed that Fan (the brother) called Qiongnu, Qiongnu 妹妹 whilst she called him Fan 哥. Fan and Kangning are twins but if I remember correctly I think I’ve heard Kangning call Qiongnu 姐姐 before and now I’m curious about how old all of them are at the beginning and the end. I don’t think we outright get told any of the character’s age but there are some hints.

• The only semi confirmed age is Jiaojiao (2nd Sister/Fuhui and Fan Lianghan’s daughter) who was born before the time skip in ep 35 and about 3 years old
• I believe during, the Shouhua and Du Yangxi arc, when Madam Du is upset with Yangxi says she raised Yangxi for 20 years 
• We know that when Shouhua should be over 20, she married her first husband she was 15, they were married for maybe a year or two and then we know she mourned him for the full 3 years and then there is the time between then and the beginning of the show
• Chai An is older than Fan Lianghan but is younger than Shen Huizhao, Chai An and Du Yangxi should also be around a similar or the same age

SPOILERS ahead!!!

Yeah, the show drops some interesting hints about the ages. If we go by Northern Song standards, minimum legal ages for marriage were ~15 for boys and 13-14 for girls. However, since the drama is a modern take on the Song dynasty, it wouldn't be odd if they raised the age of all the characters from the typical Song standards. I tried to gather a bunch more hints in addition to the ones mentioned by other commenters. 

Shouhua and Du Yangxi
• Shouhua is the eldest. She married at age 15, shortly after(?) her father's death. Her husband died less than 2 years later. She mourned as his widow for 3 years. Then there's the time between then and when the official story starts.
• Du Yangxi was raised by Qian'er as her son for 20 years. We know in reality his birth mother died shortly after giving birth to him, so he can't be much older than 20 years when he enters the story. By then, just less than a year or so had passed since the drama started.
• In ep 14, Shouhua mentions she is "several years older" than Du Yangxi (eng sub). The traditional Chinese subs translate more like: "How old is my husband?" I guess implying that she's much older than him. In English, "several" is three or more, so she's at least 3 years older if we take the eng sub literally.
• In ep 20, Kangning mentions the supposed "illegitimate son's" mother had 16 years to claim his lineage, meaning he must have been born at least 16 years ago, and was supposedly conceived around a month after Master Li died. Of course, this is speculation because we don't know if the Wu boy lied about his age, but for the sake of argument, let's say they're telling the truth about his age: ~16 years. By ep 20, we're in the second winter since the drama began, so roughly 2 years have passed since then, meaning Master Li died roughly 16 years ago. If Du Yangxi is 20 years old by ep 20, he would have been around 4 when Master Li died, making him just about 10 years younger than Shouhua (wow they weren't kidding about the age gap).
• If the above is true, then in ep 35, Shouhua would be 34-35 years and Du Yangxi 24-25 years.

Fuhui and Fan Lianghan
• One of the promos said that Fuhui married young, so she must have been at least 15 years old if they say Shouhua was considered young when she got married. She's likely in her late teens to early 20s when the drama starts. This would account for her having been married to Fan Lianghan for a while before the Li family arrived in Bianjing. It would also put her at a more comfortable age for pregnancy from a modern audience's point of view.
• Based on when Master Li died, the largest age gap between Fuhui and Shouhua could be 11 years, but I'd say she's much closer to Shouhua's age because the youngest sisters defer to her, Shouhua, and Kangning. If we include all possibilities, she was anywhere from 4-14 years old when her father died.
• Fan Lianghan was probably Fuhui's age or older when they married. He's younger than Chai An by 30 minutes, older than Du Fangxi, and younger than Shen Huizhao. Not sure of his age compared to Shouhua; the eng sub translates his addressing her as "oldest sister in law." He'd also be old enough to establish his career but young enough to make significant advancements.
• Fuhui would be anywhere from 18-28 in ep 1, making her 25-34 in ep 35. Given her close relationship to her older sisters, I'd put her as closer to Shouhua's age.

Qiongnu and Fan'er
•  In ep 3, Fan Lianghan tells Chai An that Qiongnu was 3 when her father died, and 6 when she was left at the Li house in Luoyang. She's presumably close in age if not older than Kangning, since she calls her "jie"/older sister. Whether it's an inside joke, affectionate term, or literal, I couldn't confirm. There's also the power imbalance since she's an adopted daughter, so I'm unsure how age vs social position factors in.
• In the flashback to Master Li's death, Qiongnu appears at the table with all the sisters, so Fan'er is presumably "dead" by this point, and we know she was 6 years old when she was left at Li house.
• Qiongnu is either older than Fan'er and Kangning or slightly younger. She is probably close in age, given she's of similar height to Kangning in Shouhua's flashback to when Master Li's died. However, this would put her on the older end of marriageable age by ep 35, if Kangning is already married with kids at this time (by Northern Song dynasty standards, anyway).
• Li Fan'er is Kangning's twin, but she calls him "ge", meaning he's the older twin. He "died" young, either before or shortly after his father's death, but definitely after Kangning's flashback to her father picking plum blossoms (Master Li tells Kangning she must support her brother and sisters). If he's close to Qiongnu's age he'd be around 6-7 or older when he went missing. If we use that as his base age, ep 20, 16 years have passed, so he'd be at least 22 years, making him ~26 in the final episode. But that would mean Kangning is older than Du Yangxi, so maybe not...?
• But then again, the largest age gap between Fan'er and Shouhua would be 12 years.

Kangning and Chai An
• Kangning's hair was down at the start of the drama, and she started putting it up by ep 3-4. If we take some creative liberties with the Northern Song dynasty customs, this would indicate she is of marriageable age and looking for a husband, compared to ep 1. Given that she has children during the 3-year timeskip in later episodes, she would at least be in her late teens or 20s at the time, and by then, at least 3 years have passed since the start of the drama.
• If my previous comment about Fan'er's age is right, Kangning is around 6 years old when her father died, making her at least 26 years old in the final episode. That would mean in ep 1 she'd be 20, making her older than Du Yangxi, so maybe not...?
• When Master Li died, Kangning would have been anywhere from 12-2 years younger than Shouhua. Since she's the third sister and unmarried when the drama starts, I'd think she was closer to 17-18 in ep 1, 18-19 in ep 20, and 24-25 in ep 35. Wait, so maybe she is Du Yangxi's age after all...?
• Chai An is older than Fan Lianghan but younger than Shen Huizhao. There's no confirmation if he's older or younger than Shouhua, but given he's of prime marrying age at the start of the drama, I'd be comfortable placing him in his 20s. It would also make for a more comfortable age gap with Kangning for modern audiences.

Haode and Shen Huizhao
• Haode is older than Leshan, but given how close they are, it wouldn't be far-fetched to say they're close in age, maybe 1-2 years apart.
• Haode is at least a year younger than Kangning. In Shouhua's flashback, she and Leshan are seated at the table, and neither of them really reacts to the ravaging of their household, so she would've either been too young to understand or old enough to understand and frozen from shock/fear. Her hair is still down right when she gets engaged, which confused me because Leshan put her hair up before her, despite being younger, so maybe Song Ji Li hairstyle ceremonies don't factor into the drama. But anyway, she'd be at least 14-15 years old by Song standards, but for a modern audience more likely 16+.
• In ep 20, when Haode marries, she and Shen Huizhao are seen walking by the lotus pond at the Shen house. The lotus flowers are starting to open, and lotus flowers bloom in summer, with peak blossoming seasons being July-August. Suppose this was a deliberate indication of time. In that case, we can assume they married in either the late spring or early summer after the lawsuit with the Li relatives (which happened in winter, though it is unclear how long the case took since the Li relatives appeared in December). At this point, Du Yangxi is ~20-21, and Shouhua ~30-31.
• The largest age gap between Haode and Shouhua is 14 years, but I'd say more like 13 years since she and Leshan were likely not infants when their father died. The smallest age gap would be 3 years, but given the flashback, I'd say the age gap is closer to 13. This would make Haode at least 15 in ep 1, 17 in ep 20, and 24 in ep 35. Of course, this is only the youngest she could be in this scenario. 

Leshan and Yang Xian
• Leshan wears her hair half-up-half-down (kind of) until ep 20. If hairstyle has anything to do with age in the drama, it would make sense that she was too young to seriously consider marriage in ep 1 but be at an older age by ep 20.
• Leshan must have been at least 15 years old when she married (by Song standards), and by then, at least 2 winters had passed since the start of the drama, meaning she could have been as young as 13 in ep 1. This would track with her more childlike behaviours in ep 1, and her wearing her hair down until she and Haode started seriously looking for suitors in ep 20-21.
• In ep 28, when Leshan is married, the caption reads: second day of the third month, so it's presumably the following spring after Haode's wedding. It could be later, but for simplicity, let's say it is a year after Haode's marriage, which makes sense if Leshan has just come of the ideal marriageable age.
• However,  in the flashback to when Master Li died, all 6 Li girls could be seen at the table. Leshan cannot be more than 15 years younger than Shouhua since Shouhua is 14-15 at that time. Leshan and Haode were old enough to be toddlers but young enough not to leap into action when their house got burglarized. They also didn't leave the table when the older girls got up to fight.
• The largest possible age gap between Leshan and Shouhua is 15 years, but in the flashback, she is clearly not an infant when her father died. So logically speaking, the largest possible age gap is 14 and the smallest 4 years, but as with Haode, I'd say the age gap is closer to 14.
• I'd say Leshan was at least 2-3 years old when Master Li died, generously speaking, since she had enough hair to put into buns and sit comfortably at the table. If so, she was at least 15 in ep 1, 17 in ep 20, 18 when married, and 21 in ep 35. She would be old enough to have married already, but still relatively young enough (by the drama's standards) to safely remarry without total social annihilation. This would put her at about the same age as Haode when she was first married. It's also probably comfortable for modern audiences to accept Leshan marrying at age 16-17 than at the 14-15 Song standards.
• I have no idea yet where Yang Xian fits into the mould, but he's definitely older than Leshan and Haode. He was okay with taking Kangning as a concubine in ep 4, so he's probably Kangning's age or older. However, as this drama shows, it's not unheard of for a man to be younger than his partner, so he might even be younger than Kangning...?

And don't even get me started on how in East Asian cultures, you're considered 1 year old when you're born, and generally considered to get 1 year older each New Year's. That would mess up the already messy math. I counted character ages by Western standards, so do with that what you will!