I've only been teaching for 2 and a half years, but I'll answer your questions the best I can!
How possible is it to make a full-time career as a TEFL teacher?
Getting work is pretty easy, getting paid well is the hard part.
Is it usual for a TEFL teacher to teach in many different countries?
There's no "usual" TEFL teacher, but moving around and teaching in lots of places is not uncommon at all.
What is the typical annual salary for an experienced TEFL teacher?
Depends primarily on your location, experience, and clientele. "Business English" pays better than General English. Like any teaching, it's hard work that requires a lot of preparation outside of your billable time so you won't be paid for 40 hours a week. 25 hours/week is considered full time, you have to be extremely well organized to pull off more than 32 hours/week and you won't be able to do it for very long. Generally, your wages will be on the low end of sustainable wherever you are.
Would it be possible to get a job as a full-time teacher in a foreign school with just a TEFL diploma?
If you have a college degree and a CELTA (or equivalent) and most importantly, you have a residency and work visa for the country, getting a job at a private language school should be no problem.
Does having a degree (esp in a foreign language) help you to get jobs/higher wages, or on average is it possible to be just as successful as a TEFL teacher with a normal TEFL diploma?
I haven't been teaching long enough to tell you what happens to your salary as you get more experience. My hunch is that private language schools just pay all their teachers the same. Having higher degrees (Master's, PhD's) in education or languages will start to open doors in high schools and universities (you have no chance getting in without a higher degree) and even then getting a job at a good school anywhere in the world is no easy task.
I'm not trying to be negative, but teaching is just generally not a field where you make a lot of money. And there are lots of private language schools that scam the teachers as well as the students. I just want you to go in with your eyes open.
I absolutely love teaching English, I find the subject and the people I meet fascinating and I want to make a career of it. By sticking with it I hope to make contacts with people and companies where I want to work and who want to work with me and will pay me more to keep me around. I'm also developing relationships with private students and trying to build an online strategy to generate more contacts and privates. I want to get a MA TESOL and hopefully be able to get a foot in the door at some high schools and universities. It's not an easy career, but I find it intensely rewarding and if you like doing things your own way, I would recommend trying it!