Привіт! If I say "I'll go home", will I say дім, вдома or other version of this word?
whereto? to one's place - додому, to some house - до дому
Wouldn't додому and до дому sound the same in conversation?
They would, but it's not a problem. "до дому" exists so that you could insert an adjective here: Я йду до старого/нового/батькового дому :)
On the “where? Вдома» I’m expecting it to be вдомі for locative. Please tell me where my thinking is wrong!
May I say "I will at home"?
That sentence makes no sense in English
you forgot the verb here :)
"screw you guys, I'm goin home"
So this can't also mean, "I'm going home?"
Not really. Of course, we can imagine a situation like you are leaving some place and say: "я буду вдома," such that everyone understands that you are going home right now. But you do not say that directly.
The preposition at is optional in English. If not used, it is understood.