Re: the birthdays.
The photo of TK was taken on his 1st birthday (1991). So, he was born on June 4th, 1990.
JH was born (according to his resume) on July 1, 1990.
I truly believe that this is significant. Or, it WAS significant but the writers may have decided to go in a different direction.
As far as I recall, these two characters are the ONLY individuals that have a firm "birthdate" shown in writing (or on a calendar) on the show. There MUST have been a reason for this originally. It is the most significant reason I think that originally there was going to be a "fraternal twin" story arc.
But once "strawberry" was thrown into the narrative very late in the drama, perhaps the writers decided on a different resolution for joon ha's family history.