L.R.
E., these questions are best answered by your local school district offices. Get in touch with someone there. Since you are from another country and this is all new to you, just reading the web site may be more confusing than helpful (unless they have a truly great web site!) because the information may be written with the assumption that people reading about the schools already know the basics.
Call and make an appointment to see someone and explain that you need a lot of basic questions answered in person. Don't let them just say "Oh, you have to go to the web site for all that."
If your concern is that the numbers of students in a school are dropping-- that has nothing to do with quality of education in most public schools. I actually would love it if the numbers in our school system dropped considerably because it would mean each teacher had smaller classes and could give kids more attention!
If you are talking about public schools, there will not be any fee -- they are free to everyone -- so you cannot judge a school's quality by the expense of its fees. Also, in many public school systems you have no choice over which school your child attends; your child has to attend the school closest to your home or the one designated for your neighborhood. But it sounds from another post here as if your situation in Arizona may be different (open enrollment) so you must check and find out.
Your child is still young enough that you probably do not need to know much about preparatory academies or vocational schools for a long time yet - but you are smart to start getting information. Again, your local school system can probably help.
If you are looking at private schools rather than your state or county's public schools, try to find a web site or local parent group that knows about the particular private schools you are looking at.
I know some folks recommend web sites that do "reviews" of schools but those sites can have outdated information. And sites with parent-written reviews can be full of negative reviews from parents with their own issues. So if you look at reviews onliine, just remember that the reviews may be written by people who had one bad experience that may never happen to you.