American cockroaches?

Question

can they climb smooth surfaces

Answer 1

Yes. The sticky substance on the tip of its feet allow it to climb many types of surfaces, rough or smooth.

Answer 2

Question is too vague, but in general yes. I don't know whether their "feet" have sticky pads, but I've never seen a surface that defeated them.

Answer 3

Yes, rather easily.

Even their p**p and such are deposited and virtually stuck to a vertical wall, at times.