The 4-piece bonus effect does not stack with itself. The 4-piece set bonus effect is not activated by Swirls on self, such as from the field of Dandelion Breeze.

Does instructor 4 set bonus stack?

The 4 piece bonus gives 120 elemental mastery to party members for 8s. It does not state whether it can stack or not.

Does Wanderer's troupe and instructor stack?

2pc Wanderer's Troupe + 2pc Instructor

Wanderer's Troupe has the same 2pc bonus as the instructor's. Hence, stacking these will make Kazuha unstoppable in reaction damage.