For the first question, do we care what the first card we pick is? Then given the first card, how many choices do we have for the second and then the third.
For the remaining two, thinking about Combinations from probability. There are 52 choose 3 possible combinations. To get two different suits we just need to make sure that we choose 2 from the same suit. Can you see where to go from here?
For the last question, again do we care what the first card we pick is? Then once we choose the first we have a limited number of choices for the second. Then after choosing the first two, we have further limited choices for the third. So we can pick any of the 52 out of 52 for the first. Then we need a different suit, i.e. one card out of the 39 left which are different suits. And now how many can we choose for the third?