Of course! But first she should receive a formal firearm safety training program. Adult supervision would be mandatory. Also, all local and state laws would apply.
Personal choice? This questions gets into the murky area of how much influence can outside opinions have on the way you raise your child. It's really up to you, and the values you want your kids to adopt. The other underlying issue is probably gun control which is a divisive topic.
Depends. Not all tweens are alike. Shooting sports can provide a great opportunity for exposure, reduction of fear and to learn safety, whether or not one decides to own one for self protection from those with more evil intentions. Teaching a child to shoot is often a nbinding experience that can promote principals of responsibility, safety, and skill development. But, need the right teacher and student.