Correct - as long as the angles are measured from the edge of the canal.

Not quite - you want to add the horizontal components of the two vectors. You already know that the magnitude of the 15-degree vector is 66 pounds (not 50), so you get:

F_Total = 50 * cos(20) + 66 * cos(15)

This one is so poorly worded that the ambiguity makes it impossible to understand teh geometry of what's going on. Given the handle is at 30 degrees to the horizontal - are we to assume that the force being applied to the cart is at 30 degrees to the horizontal? And since the cart is on a 30 degree incline to the horizontal, does that mean that the handle - and force - are actually in-line with the cart (since they're all at 30 degrees to the horizontal)? If there's a figure for this problem it would help to post it. But to give you a hint here - the work done will be the product of the force applied times the distance traveled by the cart times the cosine of the angle between the force and the direction of travel.