K7BMG Pretty much covered your questions already.The ATS can be controlled by using more or less light hours as well.
Typically you want the ATS and or fuge to run opposite the tank lights.
This helps to keep PH stabilized.
To cycle the rock it needs to be in Saltwater. I recommend using the same salt mix and salinity level. 1.026.
No, not all rock is the same.
Online sales from a retailer should be as advertised.
Online from Craig's list, eBay, or other private sale is a whole different issue.
Dry rock at MY LFS (Local Fish Store) is $3.00 a pound.
Live rock at MY LFS is around $5-6 per pound.
Private sales are fine as long as you can trust the person selling it.
If you don't know the history I would pass. Some will disagree but YMMV.
Ideally you want fully cured live rock. If your local to me I have plenty. If not try to find a local reefer to give you a few pieces in exchange for some of your dry rock. Most will be honest if the have pests you need to worry about.