What kind of Belt does the 2005 Toyota Corolla CE have and what would be a fair price to have it replaced in Oakland, CA?

What kind? Are you referring to the serpentine belt? Without looking it up the belt might cost $40 and it would take about an hour of labor. I am guessing a shop would charge around $200. Dealers would be more.

Thanks, Is there a timing belt? This one is squealing - does this belt run the alternator, the AC and anything else? Would the car not start or not run if it were to break?

I remember my dad using some sort of spray on his belts, but the car place said it would just make it break faster??

Your car does not have a timing belt. The squealing could be a bad belt or the power steering pump. The serpentine belt runs the alternator, AC, power steering and probably the water pump too. If you drove it without the belt you would not get far.