if my bank or credit union fails, would I still be able to use the money I put on my secured credit card or would I get a check in the mail for the amount I deposited?

Your security deposit would not be lost. The card would probably be closed, and you would get back your security deposit, minus any remaining debts on the card when it closed out. If the debts on the card were more than the deposit, you would still owe the card.

Yes

Get insurance quotes

yes they are insured by fdic

It's not the "card" that is secured. It's the associated bank account.