Car: I don't think anybody rents cars in India. You get hire a driver or an auto-rickshaw cheap. Your hotel will certainly have contacts. I think this is partially due to the chaotic road rules.
Bike: Don't know but doubt you would need any kind of license. The way some people in India drive I'd wonder if auto licenses were required.
Clothes: Get them there if you'd like. There are plenty of small stores by the beach that sell beachwear. I didn't buy any but I'd imagine that you will save some money.
Credit Card: Safe to use in any of the tourist areas and hotels. Just use the usual security measures and check your bill when you get back.
Enjoy Goa. It is a very pretty place and very worthy of a visit. It still has quite a bit of Portugese influence, and the beaches offer wonderful relaxation. Maybe you will get to see a sacred cow lying of the beach chewing its cud...^