No problem, I know a lot of this stuff was a bit confusing when I first started playing here.
I'm not sure where you're doing the red clock, but the place to look is next to their name near the top while in the game. Right now when I look, they have about 11 hours and 50 minutes remaining to play. As soon as that timer hits negative, you should see the option to expel them (and it should be near the little "what can I do?" text you were talking about).
In terms of the total time allowed in turn based games, that varies. I'm not familiar with changing a game from real time to turn based, but if it's like creating a turn based game, there should be drop down boxes with options ranging from very slow (1 turn per 2 days) to very fast (24 turns in a day). (I think you can also choose no time limit, but that may be limited to "with friends games, can't remember for sure.) I THINK it defaults to 1 turn per day (the second slowest) if you don't manually change it.
And then, each of those game speeds has a starting time allotment. I think 1 turn per day may start at 48 hours? I don't create slow turn based games, so I'm not 100% sure. But I know the fast games start at 12 hours, and I'm pretty sure I've seen other people's games go up to 2-4 days. Then every time a player starts a new turn, they get time added back (based on the game speed) to that timer, but the timer can never go over the initial time that was set if that makes sense.
The only thing is that in "slow" turn based games (anything 4 turns per day or slower), the clock always counts down during a players turn. In "fast" turn based games (8 turns per day or faster), the clock only ticks down during a 12 hour period set by the game creator (so the clock doesn't count down while people are sleeping).
I hope that helps, but let me know if I've explained anything poorly!