OK, to find (a) you'll need to calculate the marginal densities of Y1 and Y2. You have the joint density, but you'll need the density of Y1 and the density of Y2 so you can calculate E(Y1), the expected value of Y1, and E(Y2), the expected value of Y2. Are you familiar with this?
Note, you'll also use the marginal density of Y2 to solve for your conditional distribution in part (c).
Hope that helps. Good luck!