Yes, rough surfaces will wear out your mousepad faster.

Yes.

The rubber or foam backing on most mousepads is soft and grippy. Drag that across a rough wooden desk every day—especially with any lateral movement—and you’re basically sanding the backing off. Smooth surfaces create less friction, so the backing stays intact longer. If your desk is raw wood or has a heavy grain, you’re accelerating the peeling by a lot. A pad of decent quality will still last, but expect to replace it sooner. A desk pad or a thin sheet of plastic underneath can buy you time.

Unless you like replacing mousepads every six months, put something smooth under it.