cut back / thin-set

Hello...considering the Allure Ultra flooring for Dining Room and Kitchen. After removing carpeting and tiles in DR I noticed the tiles were installed using cut-back...an oil based "glue" which is not removable in its entirety. I'm somewhat skeptical about the thin set in the kitchen as the glue responds to warm water easier than chemicals. I would like to place the Ultra flooring over both. The floors are level and smooth, trowel ridges in cutback can barely be felt, rooms square. In the DR, I have removed the carpet tack strips which left small holes against the wall as well as the "entry" between DR and kitchen. I was told by sales person at HD that nothing needed to be done with these holes and could lay Ultra flooring on top w/out problem. I guess the basic question is if I need/must do anything to the floor I'm installing the Ultra upon as long as it is completely clean and free of any grit, sand, dust, dry wall remnants, etc.? And, how in the world do you paint and install molding later w/out ruining the new flooring? Please advise and thank you.