What kind of caulk should I use for sealing windows to drywall

Removing the sheetrock will lower the finished stool height a bit which will help maintain a more even reveal on the window, and make it look less like the stool was added on. Cut around the edges first with a utility knife to minimize damage to the surrounding jambs & wall below and then just pry it up.

If you really want to keep the same reveal as the old sheetrock, you could build up your new stool out of 1/2" thick stock (assuming the sheetrock was 1/2"). Make one piece that is the size and shape of the entire stool, then thicken it where it projects out from the wall by laminating another 1/2" thick piece underneath.

Single glazing with storm windows absorbs sound reasonably well, I would not expect a huge decrease in sound level with triple glazing, but certainly not an increase. Single glazing alone is another story, it's sound absorption is terrible.

The increased sound is certainly due to the frames and adjacent construction. While there is often a correlation between thermal loss and sound transmission, sound is much trickier to manage well. It is sometimes counter intuitive. The construction joints must be carefully detailed. The general concept is to avoid any solid connection between inner and outer surfaces. Any connections should be via resilient, absorbent materials. Typically, you want to fill any voids with sound insulation, though in some cases this has been worse than a simple air gap.

Also consider exterior sound attenuators. Walls, fences, trellises, large shrubs, trees, berms all will help attenuate sound, but when you consider cost vs. benefits, such measures need to be carefully considered.