No. You can simply just not read what the other gender wrote.
I think this site would be a bit frustrating for some users if you had to deal with trying to answer a question, only to find out that you were blocked. Imagine if that happened a lot while you were browsing through this site. It would make it not user friendly. It definitely would discourage users from wanting to be on Gag.
No. Everyone can have some very good and valid information to share, regardless of what the asker wants to know. Gender simply doesn't matter most of the time. If you want to target a specific gender, then simply focus on the answers you get from that gender, and ignore the ones you get from the other.
There's no need for that. I like to see both genders answering a question for two reasons: the opposite gender often has a different perspective on the topic, and you'll get way more opinions overall when everyone can answer.
I would oppose it as that would enable some people to ask some pretty stereotypical questions without at least there be some form of concern. For example, lots of guys think that there is actually some deep underlying differences between man/woman, or whatever, but behaviours the same from person to person if you look at some crucial features of the brain. I guess what I'm trying to say is, it's a categorical mistake.