If you dont have a membership card is it possible to still shop at Costco?

No you can't.... unfortunately you have to be a member. Also the membership is 120$ a year for a executive and 60$ for regular membership and you have to use a visa credit card to pay.

You must be a member to make purchases, however if you have a Costco gift card they will honor that and let you shop. I think you can probably get into the food court without being a member.

You can go in and make purchases at the food court

No