Handsome oppa interview with Viki was fun but also frustrating: the questions weren’t really related to his acting. I wanted to know how he approached Mo Tae Gu, how he related to him, what’s his view on the past of this character, on his relationship with his father, what does he think of the attraction he had for Kwang Joo? Maybe it has been asked in other korean interviews, which haven’t been translated, but it feels like he’s still considered as a sexy man rather than an rising actor

Mmmm, he’s had lots of other interviews (all in Korean, obviously) but this is a translated one that touches on how he felt about the character and the drama.

Here are some other interviews that are in Korean but that I thought were good and discussed his thoughts on the character (and other things), if anyone wants to try and muddle through them: 1, 2, 3, 4, 5, 6, 7, 8, 9

Some brief points, based on your questions above:

• He was given a lot of freedom to interpret the character and drew inspiration from Christian Bale’s character in American Psycho.
• He was not particularly sympathetic with his character, since Tae-gu was a murderous psychopath, but did want to approach the character in a way that would make him seem charismatic and belonging to the upper-class.
• He wanted to make sure Tae-gu’s personal philosophy was clear so it didn’t just seem like another random lunatic (referencing the Joker from The Dark Knight as an example). 
• He was satisfied with the ending and scoffs at the idea of returning for another season because Tae-gu is dead (yes, according to him and the production staff, the ending was literal and not a hallucination), but thinks Voice could have another season with a new villain.
• While I don’t recall any specific mention of his thoughts on Tae-gu’s childhood or father (except he was grateful to have scenes with Lee Do Kyung, because so often his scenes were shot where he was alone), there was one interview where he said he warned his actual parents not to watch the drama so they wouldn’t be disturbed by seeing their son brutally kill people.
• Any chemistry between Tae-gu and Kwon-joo during that last rooftop scene was by accident – he was just focused on portraying the emotion of his character.

The point of that Viki interview wasn’t to be hard-hitting or in-depth (after all, it’s Viki) – it was just for fun. I was most delighted when they asked about his kitty and pup (and one of those interviews mentions somewhere that if he had the ability to hear sounds like on Voice, he’d like to be a pet detective and reunite lost animals with their families).