Is it possible for the frictional force to increase the mechanical energy of a system? If so, give 2 examples with brief explanations. If not, why not?

Answer 1

Yes, but it depends upon what you call the "system". Objects falling onto a conveyor belt are accelerated while they slip, slide and acquire the velocity of the belt.

An accelerating car can be considered to be accelerated by the road friction on the tires.

In these examples, the acceleration is done by frictional forces, but the energy comes from elsewhere.