The probability of drawing a red heart is 1 in 4. This is the same as the probability of drawing a heart, as red is included as a superset of hearts.
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This is a conditional probability, given the card is red, what is the chance it is a heart. Since there are 2 red hearts, the probability if 1/2
The probability of drawing a red spade is zero. There are no red spades in a standard deck.
The probability is 7,893,600/311,875,200 = 0.0253
Assuming you refer to a normal deck of playing cards, either 0.481 (with jokers) or 0.5, one-half (without).
Probability of getting a King is 4/52 = 1/13. Having drawn the King, for it to be a Red King, the probability is 2/4 = 1/2. Hence the conditional probability is (1/13)x(1/2) = 1/26