I'm really glad you're so taken with Matt! I'll get back to him, but wanted to answer the other questions first.
The game is set to take place over eight weeks, ending at Halloween. Each "chunk" of the game covers one week except for the first two days, and each chunk has its own theme around which all the storylines during that week revolve. So for instance, Week One is The Morning After/Getting to Know You. Currently I'm wrapping up Day 2 - part 2 of 10 - so we're still very much at the start of the game.
Right now I have to work entirely solo, so if that remains the case, the full game won't be for a couple years. But I hope as time goes on I'll have enough funds to hire people to help with things like coding, testing, sound, etc., which would help cut that timeframe down.
Okay, to Matt! You have the right idea of it as far as feelings that might be happening. I have a key moment planned for the first time he & Connor get together that will clarify things quite a bit. I don't want to give away too much so early, but I think players who are into Matt will be happy with certain revelations during that scene. Overall Matt's story gets a little complicated, though, possibly in ways that won't be expected. Not everyone's happy ending looks the same.
I won't be doing poly relationships simply because doing couples is complicated as it is with how much the storylines can change. Threesomes, sure, but full romantic relationships isn't in the cards currently. Though I think you'd be right about Owen being a good candidate.
The next release - The Club Update - doesn't feature Matt but does have Matt content, including 8 new CGs. A new main character is introduced named Griffin who has ties to Matt, and spending time with him can reveal some interesting things. Connor does indeed mull over how it feels that his best friend is kind of a different person now.
So when that comes out, the path to play through if you want Matt content is hang out with Matt in the afternoon, proposition him without backing down, then head to the club and spend as much time as you can with Griffin.
Lastly, since the game will only cover two months and relationships won't be fully defined until the end, Connor won't be moving in with anyone. I image if he does get serious with Matt he'd probably move in with him at some point, though!