The best way to calculate the probability of a certain event is to use this formula:
# of possible outcomes / # of total outcomes
The first question would be:
4 queens / 52 cards = 1/13 = 7.69%
The second is a little trickier. We need to think of all the cards that satisfy the solution. We have 26 red cards total (13 hearts, 13 diamonds). The red queens are already included in those numbers. So we'll add the other two cards that satisfy the requirement: the 2 black queens.
28 cards / 52 cards = 7/13 = 53.85%