The following is compilation of info from Wikipedia, Namu Wiki and a handful of facts collected thru Episode 3.  Definitely subject to change.  SPOILERS!

Main Characters

Modern Era: Shin Seo-ri

Once a successful child actress, Shin Seo-ri is unable to continue that success as an adult, eventually taking odd jobs and stand-in roles.  While filming a poison scene for a historical drama, she becomes possessed by the spirit  of the Joseon-era villainess Kang Dan-shim and develops a vicious personality.  

• Joseon Era:  Kang Dan-shim - Dan-shim’s reputation was as a ruthless and cunning concubine [Huibin Kang] of the Joseon dynasty, known as the most reviled villainess in the court. She rose from low birth to the position of first-rank concubine without strong support, leveraging her sharp wit and manipulative tactics. She had an incredibly strong sixth sense.  Upon royal decree, she was forced to drink poison, but prior to that a shaman told her that in order to live, she would need to die.  As she lay dying, she thought of Prince Lee Hyun and wondered “perhaps this is. . . .?"

Modern Era: Cha Se-gye

The infamous third-generation chaebol heir to Chail Group and CEO of Biojei, he is known as a "monster of capitalism".

• Joseon Era:  Grand Prince Lee Hyun of Cheongheon, the youngest son of King Mujong and younger brother of King Anjon.   When the first brother died mysteriously in the fire at the East Palace Library, the only survivor was young Hyun. It was then that a shadow began to cast a shadow on Hyun's life. After leaving an scar in the corner of his eyes due to an accident, he put on a half-mask.
  
  The second brother was suddenly appointed as the crown prince, and Hyun had strange nicknames, such as The Ghost Prince with the Damaged Eye and The Blood-drinking Goblin Prince. 

Modern Era:  Choi Moon-do

The president of Chail Construction and Se-gye's cousin. He made repeated efforts to gain the attention of his uncle, Cha Dal-su. He also volunteered as a liver donor for his uncle, who was suffering from acute liver failure. After becoming President of Chail Construction, he deemed the role insufficient and continued to pursue his uncle's position.

•  Joseon Era: King Anjong, the 2nd son of King Mujong and the 2nd queen Min.  He has the blood of his [older?] brother on his hands in order to ascend to the throne. [Queen Onjeong is  his wife?]

SUPPORTING CAST

People around Seo-ri

Nam Ok-soon - Seo-ri's beloved grandmother, who raised her since she was a child

Baek Gwang-nam - Seo-ri's next-door neighbor who becomes her manager

Yoon Ji-hyo - A top star with 19 years of experience in the entertainment industry.

Hong Bu-seon - CEO of Doran Entertainment

Kim Jeong-ae – a modern day shaman/fortune-teller that tells Seo-ri that she is possessed by a spirit from the Joseon era

            Joseon Era: Kim Bo-sal was a shaman that told Kang Dan-sim that in order to live, she must die.   

Gu Pil-gyu – manager of Seo-ri and Gwang-nam’s apartment building

Kwak Eun-ah - Seo-ri's fellow actress

People around Se-gye

Son Jae-chan - Se-gye's right-hand man

Kim Hyun-hee (Secretary Kim) - Se-gye's secretary, who is raising two children

Mo Tae-hee - The precious [spoiled] daughter of Mo Chang Group, who is Se-gye's blind date [Side note: I wonder if she will be reincarnation of Queen OnJeong?]

Cha Dal-su - Se-gye's grandfather, who is the Chairman of Chail Group

• Kwon Jin-ok, the butler in charge of the affairs of Dal-su's mansion

Jang Seok-ho (Director Jang), a Biojei executive, who was once a founding member of the Chail Group

Cha Ju-ran - CEO of Chail Food and Se-gye's eldest aunt

Cha Ju-mi - CEO of Chail Apparel and Se-gye's second aunt

Sunwoo Jung-hyun - Se-gye's friend and a psychiatrist

My character charts are based on "facts" - 95% from official sources (SBS web site, Namu-wiki, etc) and 5% from the drama such as the name of the Queen. i will edit as facts are revealed or revised.

But no problem speculating or questioning the drama itself.

As for recognition, I think that Dam-sin rarely looked directly into Grand Prince Lee Hyun's face - it was simply not done back then. He kept ordering her to raise her face - but mainly so that he could look at her. She continued to keep her eyes cast down. Anyway, that's my theory.