Will “Thief Gloves” and the “Master Thief” specialty stack

The Sweeper counter is only increased, or lost, when you encounter parties of 2+ monsters. So, you can get to Sweeper Hero even if every other battle is a single monster battle, so long as you KO the 2+ mob parties with a single attack.

When you fully rebuild Norende you have access to some pretty sweet items, with the village shopkeepers occasionally sending you some of their stock as a gift (sadly, never weapons or armor). But besides that, you only get an extra Party Chat scene. No extra gifts as far as I can recall.