Interesting post - thanks.
I guess that possible answers are:
1. Possible combinations are; BB, BG, GG. So the probability of it being BB is 1/3
2. If there is at least one boy, then the possible options are BB and BG. The probability in this case is 1/2 for me.
3. I have to admit that I am not quite geeky enough for this one - I'm struggling to see the relevance of the birth day of the child. I'm guessing it makes it more likely that they're two boys though? I'm sure somebody will enlighten me shortly