They are looking for someone that knows about games AND has no idea what they're doing. Not necessarily, you don't always need background on the genre to be an effective tester. This kind of feedback is important. But still don't just blindly sign up for anything you see if you don't plan on actually testing and giving feedback. It's a waste of time for both you and the company and isn't a way to gain experience.
Alpha testing is quite a bit different than beta.
The general public doesn't usually participate in this testing phase. Alpha testing usually comes in after the basic design of the program has been completed. You will look over the program and make suggestions or give ideas to the designer to help improve it. Don't report the little things. There's bound to be a number of bugs after a program is created and the designer most likely knows about many of them.