The second answer is not correct: Using R I got P(X >= 1) = 0.75 and this makes sense since the probability of 0 females is P(X = 0) = 0.25 and 1 - 0.25 = 0.75.
With regards to c) you are right about independence, but you have to remember what the probability and event is here. You are only looking at one child in this case since you know that you have one daughter.
Since P(First Child|Second Child=Daughter) = P(First Child), it means you are looking at probabilities involving only one child which means you have two options: daughter or son and they have equal probability of 0.5.
Hence the final probability of P(First child = daughter|Second child=daughter) = P(First child = daughter) = 0.5