1. Normally, the Fermi level of a metal is a basic material property of the bulk, so it should not change in the presence of a contact with semiconductor.
2. No, it changes due to the image charge effect.
See, for example, here (or in any textbook on semiconductor device physics):
**broken link removed**
3. At forward bias, the barrier for electrons going from the semiconductor to the metal decreases, so current increases (nearly exponentially).
At reverse bias, the barrier for electrons going from metals to semiconductor stays (about) constant, so the current does not increase (much).