Your tree diagram is correct. But in (a) only one of the possible outcomes is favourable ( girls). So the probability of this is .
In (b), if the question means B, G, B in that order, then, again, only one outcome is favourable. So again the probability is . However, if the question means "What is the probability that they have 2 boys and a girl?", then your answer is correct.
Of course, in reality, the results of previous games cannot be used with any degree of certainty to predict future results. However, if we assume that, based on past form, the probability that your team wins a particular game is , then we can draw a tree diagram to represent the possible sets of outcomes of four games, with each outcome equally likely. (Just extend the tree diagram you had in Question 1 to another level.)
You'll find that, of the possible paths through the tree, of them result in wins and losses. So the probability of exactly wins is .
(If you're not sure what these possible paths are, here they are: WWLL, WLWL, WLLW, LWWL, LWLW, LLWW.)