2. Yes and no. Depends on the type of character you are, too. Different jobs get different premiums. It also depends on the show, if your job is union (as a face character, you are not), etc.
3. Yes and no. It depends on when you put your availability. But, you have to stick with that for an entire "block" (season) that they schedule you and once you are put in, they are not very flexible with you. As a result, I had to be more conservative with when I said I'm available. My other job is MUCH more flexible, as we schedule bi-weekly and if I need to be somewhere for a class project and know a couple weeks ahead, they are able to help me out. Disney is not.
4. Yes. Wage is not great, and you don't get enough hours. You do this job not because of the pay, but because of some other "value" it gives you. What that value is, is really up to you. It might be a "dream" job, you might like getting into the park for free, you might like the interactions with guests, etc. But it's not for the pay. Making 20/hr is rare, even with a face premium. Most people make much less.
To answer your final question, in some cases I think you can. I'm not too sure, as I don't do it, but I know there are others who have. There are some rules about how much time you can do parades, as that is not the character department. I also think the rule is parades people cannot do character work (walking around in the park, etc), but character people can do parades work on a limited basis. If a parade performer wanted to do his/her character outside of a parade, he/she would have to audition just like everyone else. If a character performer wanted to do a parade, I don't think he/she has to go to a parades audition (At least not always. It's murky to me as I know people have done it without the parade audition, but I don't know if an exception was made or not. But this does not strike me as the type of place that would make that type of exception.)