My credit union account went to collections, and I am needing another bank account (for car insurance). Without paying off that other debt to the credit union just yet, would I be able to open another account with a different bank?

What type of "account" did you have that went into collections. If this was a checking account that you did bad checks on, and it is now in collections, no you will not be able to open a new account.

Next why do you have to have a checking account to get car insurance?

It was a checking account with the credit union. Citifinancial withdrew a car payment from my account that I didn't authorize, which set me back and I wasn't ever able to catch up.

Second, as far as needing the bank account, the insurance (Farmers) that I'm trying to go through requires that automated payments be setup through a bank.