I think a lot of your confusion will be aluded by looking at the graphs of these functions.
To find the area of a, you'll need to find, which of the two functions is the top bound, and which is the bottom bound of area A. Then integrate the "top" - "bottom" from their left intersection (x=0) to their right intersection.
To find the volume of a rotated around the x-axis, you will need to integrate with respect to y. The idea is to add up a bunch of discs. The area of a disc is where is going to be the difference of the squares of your two equations. Integrate this over the length of your region. (You are in essence adding up a bunch of infinitely thin discs).
Same idea for part c, but integrate with respect to x.