Yes, sometimes they sit for hours at a time and sometimes they are very active.
You can have a small school of 3 of one species, especially if you have other corys in the tank. 3 of each species is the smallest school I'd do. Yes, larger schools are better if possible. I've read that in nature they have schools of 150!
I have 5 peppered corys and for the first 6 months they spent most of the daylight hours hiding in the plants. Now they frequently are the most active fish in the tank and often swim up to the waterline, or even upside down to eat stuff in the biofilm.
My corys have become so bold that I have to watch out not to run into them when working in the tank. I've had corys "kiss" my arm when I'm working in the tank. Give them a chance to settle in. They probably will get bolder and more active over time.