If you enter the Chinese bank, are you then able to withdraw more the at the ATM machines?

Stefanie, generally, there is no limit when you withdraw money from the bank counter. But you may need to make a reservation one day in advance for taking more than CNY50,000 cash. As for ATMs, different banks have different limit. But most banks regulates that each transaction at ATM machines should be less than CNY3,000, and one account can withdraw CNY20,000 cash a day in total.
The linking can be achieved. You can do it at the bank counter as well.