Nope. Cash only.
In fact I just looked, website lists a yahoo e-mail address, you might ask them yourself. I hope this is satisfactory, it is all I can do not being there at the bar right now. Well, it is 11:15 PM there, so I would be asleep.
Yes, credit cards are accepted!
I believe that they do, I am several months away now, from Puerto Morelos. We always pay in pesos for security reasons. It is one of the more frequently visited spots and many British and Canadians seem to come there. Usually a great band for this city anyway. Did you look for a website, even the tiny places seem to be on the web. Have a great time on your visit.
Get quick answers from Cantina Habanero staff and past visitors.