I have all of those with my credit union in the US. Heck, every bill I pay using online bill pay gives me rewards points typical to what using a CC would do. This includes paying bills where the credit union ends up mailing a physical cashiers check.
All of the above with no charges, although they may have a requirement to have direct deposit set up.
In the UK using cheques for anything is the rare exception. The plan is to phase them out within a few years, but already hardly anyone uses them any more.
It's the exception for banks, but credit unions are generally good to their customers. The few dealings I've had with BofA for example left me wondering why anyone would ever deal with them. At my credit union the people are friendly and when I used to go to a branch they actually knew me.
Free banking
No charges
No "convenience fees"
Free online banking, setup automated payments, one offs, transfer money to other banks in the UK instantly, etc
I assume you're talking about the US?