Can I use my Costco card to buy gas

If it's a bank card you can. If it's a costco card only it will ask you to insert a bank card after your costco card

Yes

You will need to have your Costco Membership card to initiate the Gas purchase, once the purchase is initiated, it will ask for a Credit/Debit Card for payment. If you have a Costco Citibank credit card, you can initiate and select the option to pay with the same Costco Citibank credit card and you will receive Costco cash back points.

Ditto

You can use your costco membership card if it is also a credit card, you can use your costco memebership card and any other Visa credit card, or you can use a costco gift card without a membership card.