Does the Greek take Credit Cards for Food and beer inside the venue?

Yes take both

Of course

My experience: yes! However there are multiple small booths selling drinks not a single bar so policies may vary.

It varies, id go with both for sure

There a restaurant's that do, I don't believe all of the kiosks however accept credit cards. The some kiosk's are private vendors who may not. I would go with both cards and cash.