"Your body - your choice" refers to the basic human right that you're your own master and no one else can own/control you.
It's especially used in the discussion about whether abortion should be legal or not, where it refers to the fact that the fetus in a pregnant person is indeed part of that person, and they are allowed to do what they want with their own body (e.g. abortion).
The post mentions the opposite, "your body, our choice" which refers to the anti-abortion movement where people, often due to religious reasons, think they should have control over a pregnant person's body, rather than the pregnant person themself.
Depends on the size of the area you're considering. In some area, one nuke would blow up 100% of the mines. But in some other, larger, area, it would only blow up 50%.
But to be fair, using nukes to clear mines is probably one of the least effective methods considering all the collateral damage on villages, fields and nature.