Was there some timeline shenanigans in this movie? Because the mentor's death seems to have occurred before the two leads met, and Woo-ram went to the funeral. Then they meet, he goes through several jobs, and eats lots of burgers. It must be at least several weeks later that he gets the call about another funeral, which Hyun-ji accompanies him on. But this funeral is also for the mentor!

Any explanations? Are events shown out of order? Or was it one multi stage funeral with many weeks in the middle? Or something else, did I misunderstand something?

It wasn't a funeral, but a memorial (death anniversary). Lots of religions/cultures have this, once a year on the date that the person died. So it was one year after the mentor died.. :)