2. I've always seen the bonuses from Unarmed and Dodge on the character screen. To check, see whether your stats change when you add points to those skills.

1. Unarmed/Staff/Armsmaster is a headache. It is my opinion (having tested this long ago, but hardly remembering it now) that you will do less damage by combining Staff and Unarmed than by putting all of those skill points into Unarmed. This is partly because the staff is a slow weapon, and Unarmed alone is very fast.

(If you're using cheats or exploits to bring all your skills up to 60, then Staff/Unarmed becomes powerful and fast enough to overtake Unarmed alone in damage dealt per second. (Not that it matters at that point.))

Let's see if I finally have this right:

Armsmaster works fully only when not using the Unarmed skill (e.g., when using Staff up to Master level). Armsmaster with Unarmed, or with the Unarmed/Staff combo, will grant its attack bonus and reduced recovery time (which are both worthwhile), but will not confer a damage bonus.