Yes they ban foreign companies. All companies need a Chinese partnership to enter China.
Eg. Azure needs to let someone else handle the infrastructure there. The only exclusion i know of ( i think) is Tesla, because China is very interested in it's tech and for it's goal of EV dominance.
They don’t, there is plenty of western companies there. And yes, they need a local branch, same way non-US companies need US branch to conduct business there.
American law forces all US-controlled companies to relay user data to various govern agencies without any real oversight. EU is protecting their citizens too.