I've heard from multiple people around here that 3D Touch works just fine with a screen protector. I don't use one myself so I can't personally guarantee that though.
I can verify that it works just fine with techarmor glass screen protectors.
Apple's official stance is that the protector needs to be 0.3mm or less. The techarmor one I use is 0.33mm.
Speigen also advertises theirs as 3D touch compatible.
Absolutely. 3D Touch is triggered by pressure and I don't think any screen protector that are out in the market today are thick enough to prevent you from pressing your screen.
Having the glass protection on the screen doesn't affect in any way force touch. Same amount of pressure either glass is on the display or not, in my experience.