You need a physical gap around the cabinets, not just for the weight on the floating room part to be severed. So, you’d need to cut, and trim off a 1/4“ piece. Not the easiest thing for a contractor to do in place, but I don’t have a lot of sympathy for someone who can’t read directions, or understand industry standards. The underlayment issue will only be resolved by removing and replacing. The extra backing has probably already damaged the locking mechanism. I‘d let him cut the floors at the cabinets. But only to remove and replace all of the flooring. And only if you put a level on the cabinets to see if having a compressive material under the cabinets had not caused them to settle and become out of level, or have other issues that will show up with the counter and backsplash.

The million dollar question is whether that water is present only when it rains, or if that is possibly the only time that you look and notice it. I agree that it looks like condensation, but the pics aren't the greatest. Water testing would be a good solution, although I'd definitely check in the morning after a cold night (no rain) if you have not already done so. It really shouldn't be hard to prove the origin one way or the other. If its dry under circumstances where condensation is likely, but produces water upon hitting it with a hose, you have you answer and I'd go back to the builder with it in that case.

Also, if the soil is getting literally all the way dry, there will be repercussions. If you have the opportunity to move it to a clay pot, you might be as pleased with the results as my Begonias have been. The breathable clay allows the soil to stay as moist as a Begonia enjoys while drastically reducing the risk of overwatering (root rot due to lack of oxygen.) I won't use plastic pots for Rexes anymore because of the dramatic improvement in the clay - except one that has a wick. Another thing you can do is propagate some leaves, so you're not counting on just 1 root system. A healthy Rex leaf stuck in water will almost always make roots. When you see a little poof of roots, bury them just under the surface with the rest of the original leaf secured in some way from blowing around. New baby leaves should start to grow where the roots are soon. For this delicate situation, I use a gentle spritz with a spray bottle to water until the roots are holding the soil in place after a while.

Yes from the shower. Moisture and hot air rise and condense at the skylite and or tunnel. Ideally a much better ceiling fan and something other than drywall for the tunnel, although that are will still get wet from condensation. One of the pitfalls of a skylite in the bathroom. You could do the plexiglass like above mentioned but it will only do so much, moisture will still get past it and it will look awful in fairly short order.