Science is a set of processes where you take belief out of the equation. You can start with something akin, which when you have informed belief you have an hypothesis which you set out to prove. You don’t hold that as truth and anything not falsifiable is not a valid hypothesis.
Science is not a religion, it’s just a thing. Plenty of people need to belief to function and end up having (even a blind) faith in science, using it as a religion.
On your second point I’m with you on the last part though I think you are calling religions and believes things that are organized religion and religion.