The most capable, adaptable, and accomplished adults I know moved around a bunch as kids. It forces you to learn how to live in the world and get out of your comfort zone. The most anxious, bitter, and underperforming adults I know grew up in the prototypical suburban bubble environment. End meaningless personal anecdote.
I still agree, and in fact kids are often more adaptable than adults. Usually they can handle change, and it is good for the mind to experience different worlds.
I guess there's a happy medium. I've heard horror stories from both ends of the stability spectrum.
I haven't lived in one place longer than two years since I was eight or so. It wasn't the easiest thing in the world, but I wouldn't be the person I am today if I hadn't grown up that way.
Depends on the country / school system. Not all kids have 3 months of "summer break."