"It is haram in Islam to wear clothing of the other sex. "
This is utter nonsense. "Muslim" is not one way of life, just like Catholic, Anglican, Jehovah's Witness, Mormon etc are not.
"Clothing of the other sex" - You mean like trousers, suits, and shorts? Muslim women wear them all the time.
"Guidelines of practicing sports in Islam for women... far removed from the eyes of men, whether they are trainers, teachers, students, administrators or spectators. ... it is not permissible to take pictures of women’s sport, so that they will not fall into the hands of men who will look at them"
Again, nonsense. You seem to have no idea that women's sport exists in Muslim countries, and that Muslim women in sports are visible, photographed, and promoted, regularly appearing in international competitions.
Feast your eyes on Turkey's women's volleyball team, who happen to be the current European champions. Their coach is an Italian man (Daniele Santarelli) and one of their star players is an out lesbian (Ebrar Karakurt). Like all other volleyball players around the world, they play in tiny shorts. They are hugely popular, photographed all the time, and they appear in ads for various products from sanitary pads to sports equipment. In their shorts.
"The game should not involve physical fighting where the face or head are struck."
Again, nonsense. I give you Turkish female boxer Esra Yildiz Kahraman who got bronze medal at the Paris Olympics a few months ago.
Your Muslim friend who told you all this sounds like a fundamentalist. You should try to meet some more Muslims whose views and lives are far more compatible with ours.