1) No and Yes (although the wording "one after another" took me a second - I think they mean that it matters).
Ok so you use combinations:
You want to pick 2 cards from 4. Even though there are 52 cards, it doesn't matter for this. You want to know how many ways to pick from the set of 5's.
2) No and Yes
You want to pick 1 from 2 cards (2 red 5's) and then pick 1 from 13 cards (13 spades)
2*13 = 26
Technically you could do
but you get the same thing. It's just the more general approach.
3) Hint: This question is really asking (since you are only picking 1 card) how many cards satisfy (either red 5 or spade)?
4) Hint: This question is really asking (since you are only picking 1 card) how many cards satisfy (either red 5 or heart)? (notice that these sets overlap).