Would triple pane give me better results than double pane in a key location (bathroom)

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.

Condensation appears to be on the inside of the window.

After 10 years, the seals have failed. They are no longer "gas-filled" - they just have air in there, and the air in there has water in it, which condensed when they are cold. The only way to fix this is to replace the double-pane unit. It's remotely possible that if your window manufacturer was optimistic this MIGHT be a covered failure (they would pay for or supply the replacement panes under warranty), but it often is not.