Is this the new click together floor they have? You should be fine with the tackstrip holes so long as it's a floating install and not a glue down. Glue down would require minor patching. As for the cutback residue, I'd seal it with some sort of tack abatement product. Apac use to make one called Tac-Abate, but it's off the market now so far as I know. You take the chance on it being sticky and causing noise if you don't seal it. You can also powder it with floor patch to absorb the stickiness. My other concern would be if any of the solvent in the glue leaches into the new floor and discolors the vinyl. I'm not sure what your reference to thin-set is here. Maybe there is a type of Allure I haven't seen.
Paint your molding before installing, then touch it up after it's on the wall. Use a paint shield to keep paint off of the floor while touching up.
Paint your molding before installing, then touch it up after it's on the wall. Use a paint shield to keep paint off of the floor while touching up.