I don't think there's an exact amount of moves you must make in the 30 minutes, 5 mins, etc., but I believe you must make a move within one minute of starting a game.
I'm not sure about your other questions, though.
You can, I think, get in trouble for not moving quickly enough in Live Chess (unlike on chessfriends.com, for example).
All the times are for the completion of the entire game, not a certain amount of moves. Standard time-controls begin at 15 minutes per side for the entire game, and move up from there.
Thanks a lot for the comments!
Ok, I get I must get my first move under way within a minute from the start. No problem. 
But trysts, what happens if say after (the initial) 15 min, the game is still in full swing, maybe even with an equal position? Is this an automatic Draw then? Or worse even, if one side is winning?
Sorry if I sound like a really stupid dude (which I honestly believe I am not). I wanted to clarify those rules before my first live game since frankly I hate to potentially get in (time) trouble because of not knowing the rules.
Just saying, I would welcome the option to play a live match with the classical chess time controls (or half the classical time, so 1 hour for first 40 moves, then 30 min for the next 20 etc.)
"But trysts, what happens if say after (the initial) 15 min, the game is still in full swing, maybe even with an equal position?"
Then whoever runs out of time first, loses
Yes, all your moves in the time control. It stinks to have a clearly won position, and lose because your time runs out on your clock, but that will absolutely happen. It's good to have maybe a ten second increment added on, that way if you get into low time trouble, you can play in the ten seconds added onto each move.
Ah, I see...
Now this is not against you of course, but I think this is just a stupid time control then. I am a bit shocked it is a simple and plain as this.
Many thanks for your help, I really appreciate! 
Tfulk,
yeah, I might go with an incremental time added game. Otherwise, this is totally ridiculous and plain wrong IMHO. Really makes me reconsider if I want to play Live Chess here...
Ah, I see...
Now this is not against you of course, but I think this is just a stupid time control then. I am a bit shocked it is a simple and plain as this.
Many thanks for your help, I really appreciate!
When you're beginning chess it's best to play longer time-controls of course. But when you get better at chess you'll see that you can play moves quicker and quicker, maybe even getting to the point where you can play an entire game in five minutes or less. So just use the slowest times possible for now. Take advantage of turn-based chess, where the time-contols are from one day per move up to fourteen days per move. Start as many games as you can handle. Good luck, haegint!
OK! Point well taken.
Actually, I am currently playing a turn-based online game here right now. Cheers!
I want to play 20 minute games, but can't find a way to chose them
Ok, so I am either extremely dumb because despite reading the various LiveChess help pages I still cannot figure it out, or I missed it somehow....
About the various time control choices... I am interested in the slower ones. I see many options, among them 30 min, 10 min, 5 min. (There are also those special formats that add back time on the clock per move made.)
So let's take the simple "5 Min" for example... how many moves am I supposed to make in these 5 min?? (I would think 40 moves)
Likewise the 30 min, is that 30 min for 40 moves?
I also have a time option called "Standardtime". What is this option? Is it the classical chess, first 40 moves in 2 hours, next 20 in 1 hour etc., like they played at the Candidates in London recently?
Sorry if these seem extremely trivial questions, but I could not find the answers. Especially how many moves are to be made in these time limits.
Many thanks for your help and patience!