Shaving in the shower does help with a quicker shave, I think it is because you can rinse your head and check for spots faster than at a sink. I sink shave and shave ATG only within 3 passes. 1st to get most of the hair, 2nd to get some missed spots, and 3rd for any final touch ups. I am a large believer in hair reduction and not to get all in one pass. Reduction is really the best way and requires more than one pass, this also is a good way to prevent or lead to less irritation of the face and scalp. Most causes of nicks/cuts and razor burn is going to fast, although razor burn can happen from different circumstances (too little or poor shaving lather, bad/dull razor, etc).
Yes, in the shower you can wash the head and get the hair soft and ready for the shave soap and the steel.