Can I open a beer shop as an FOP?

YES you can.

A natural person - an entrepreneur paying a single tax of the second group has the legal right to carry out retail sales of beer for on-site consumption, provided that he has the status of a public catering entity under the code of the type of economic activity 56.10, the entrepreneur is included in the Register under number 39 and obtains a license for retail trade of alcoholic beverages.