Plumbing – Tub re-glazed and re-caulked, drippy residue from caulking

Number 1

It could cause a problem, however it it unlikely. Use the shower a few times, and see what kind of condensation settles on the wall above the tiles. If you can see visible droplets of water beading on the wall, you will have a problem over time. As your house settles, and expands/contracts over time the grout will develop fine cracks. These droplets will over time go behind your tiles, and weaken the structure of your wall. If it was cement board it probably wont even matter, and we are talking decades before damage here, but why take the chance for a $5 tube of caulk? There are several brands of caulking meant for the bathroom that can be painted.

Tip - when you apply caulk and run your finger over the caulk to get a smooth surface, make sure your finger is wet first. Makes a huge improvement to how the caulk spreads and looks.

Number 2

The silicone will affect the drying of the grout, and you will probably find it takes well over a week to match the color of other grout. Depending on how good the seal is (i.e. is the grout exposed to air or a porous surface underneath), it could take a very long time. I wouldn't worry about it other than for cosmetic reasons.

While caulk is fairly elastic, it handles better under compression than tension. By filling the tub all the way, you expand the gap quite a bit. Once the caulk is applied and the tub drained, the caulk compresses. During normal use, the caulk will likely never be in tension. As you'd have to add more weight than a tub full of water, before the caulk had to fill a gap larger than when it was applied.

Also, there's an old saying. "Happy wife, happy life" - Unknown