Question 1. How much downward pressure can be put on the basedboard trim after installing a floating engineered wood floor over 2 in 1 pad? I want to make sure that the floating floor moves up and down as little as possible when it is stepped on and I'm thinking that downward pressure would help prevent movement.

Question 2. As far as a floating engineered wood floor goes, does a cork underlayment with a poly vapor barrier move up and down less when you walk on it than does one with a 2 in 1 pad? I assume the cork does not have to be glued down and the poly goes on top of the slab.

#1) Floating floors expand and contract sideways. Never nail trims into the flooring. Bu when installing baseboards or quarter rounds, you can push down on the trim to have a snug fit. The flooring will still be able to expand if needed.
#2) The flooring should not be "moving up and down". The substrate needs to be FLAT. Once the "pad" is installed, either cork or 2 in 1, the flooring should lay flat. Sometimes, you will get some floaters that are bowed (banana boards). The manufacturers always say they will lay flat shortly after installation. I suppose that is true for a few boards that aren't bad but if your flooring is all bowed, I would not install it until the supplier replaced it with flat flooring

Thanks for the quick reply Gary. One more question and I think I will be good to go. "Cork versus 2 in 1 pad for and engineered floating floor" What is your recommendation and why? I'm guessing it is a personal preference thing but I would like opinions.

I've never used cork. Always the manufacturer's pad. I cannot say what is better. There are some "quieter" pads available so I understand. I used an upgraded pad awhile ago on a Wilsonart floor. I did not notice a difference in the sound.