Last question first. The answer is "Yes."
Violence, especially toward women is endemic to their "culture."
Middle question on pedophilia. All? No. Most? Yes.
And finally the "Virgin thing."
It's really very simple if you think about it.
Moslem men are (especially the Arabs) desperately afraid they will not "measure up." They are therefore desperate for a wife(wives) who have not known other men. The chances of comparison are too humiliating for them to contemplate.
And, by the way, they are mostly ignorant, (literally) retarded inbreds who reply on this barbaric system without which their lives would be without purpose. With Islam they have purpose - killing and dying for he bloody Moon god.
Overheard in Jihadi kickball locker room:
"Yes, Masouud.. eat the bacon. It will make your man parts grow!"
"No! It is Haram!"
"Just look at Mohammad! See how he has flourished!"
"Allah be praised, it is true!"