and do you think the interview on the radio when he's in the taxi is about the author ?

I think writer K could've been Haaesoo & Seo (the photographer being interviewed) could've been Taekyung (the guy being dumped by Haesoo, who was bawling his eyes out at the restaurant). That was why he was complaining about not doing well in the interview. And also why Haesoo suddenly seemed to notice something in the taxi.

The boy( crying guy) that was dumped by Haesoo is not Taekyung.