Do you mean wax every 3 months? I wouldn't make polishing a regular item, as it's essentially a destructive process, like a very fine sandpaper. The more you do it, the more you strip you clear coat and eventually you won't have any left. Polishing should be done on an as-needed basis; regular washing and keeping a layer of wax on there will go a long way to helping keep that clear coat in tip-top condition.
As for paint protection, the consensus seems to be that it is in fact just wax which they apply pre-delivery the same as you and I would, except they charge you $1200 for the privilege
Regarding paint curing time, as you've said the car has been sitting around painted for quite a while before you ever get to drive it, applying some wax won't hurt it at all. I'd stop short of polishing perhaps (not that it should need it), but waxing when done properly really isn't tough on the paintwork - you can even apply it by hand if you want. It really won't hurt anything.
I think you are talking CUTTING POLISHES and no I dont use them every 3 months actually never used a cutting polish yet (maybe I should on the corolla)
many polishes are just fillers which you then add a layer of wax over the top to bring out the lustre