Interesting question. I'm repeatedly taken aback by the questions here as a native Swedish speaker who's been out of the country for some time... I know what to say, but why is a different question...
- “Ok, jag går upp på mitt rum och väntar.” (Here, could you use går upp till (or even upp i).)
I think "till" works, but I also think that the direction "upp" then isn't really necessary. So I would think either "går upp på mitt rum" / "går till mitt rum" work. "upp i" does not work.
- “Pappa kommer in i mitt rum.” (Here, would it be possible to use kommer in på?)
Maybe. See later...
- “Var är din syster?” “Hon är på sitt rum.” (Could we also say är i?)
Literally 'could'? I think so. Would we say it? I'm not sure. See later...
- “Pappa går till min systers rum.” (Would it be possible to går på/går i?)
So I think both are very unlikely to be heard and my hunch is that this all has to do with something I have a hard time putting my finger on. In the context of all the example sentences you've given "till" sounds appropriate. I could imagine an extreme hypothetical in complete isolation where you have a couple of rooms looking like cubes on a theatre stage where a man is walking literally on top of one of the rooms, and in that case perhaps you could use "på". Similarly I imagine you could come up with some situation where the focus is on the act of walking, and then we're adding where that happens - so it's walking inside a room "går i ett rum". Again, very unlikely.
So normally you would definitely use "till" here.
I think that's maybe the difference here between using "upp på" and "till". The subtle difference is that if I say "jag går upp på mitt rum och väntar." it almost sounds like an activity, in the sense of a (future) state of being, just like "Hon är på sitt rum." Vi går på bio" is also an activity. If I text you in the middle of the movie you might reply that you can't text because "jag är på bio".
By contrast then if we're talking about a moving object or person we'd use "till" and "i" etc. So even though you're saying "Vi går på bio" you're not really talking about the physical act of walking, you're talking about the activity of watching a movie. On the other hand if I'm asking you for where we're going and you want to give a more specific location which indicates motion you'd perhaps say "Vi går till Rigoletto!". In that case it's clear that you're going to watch a movie by knowing Rigoletto a movie theatre, and you're pointing out that you're going to a specific one.
Unfortunately having said all of that I don't have a grammatical answer that I'm 100% certain of... but I'm sure someone else will chime in..