Is it permissible to perform the obligatory prayer in a shop selling pottery artifacts for a tourist hotel frequented by foreigners, given the impossibility of tourists entering while carrying alcohol?

Selling pottery artifacts is permissible as long as they are not statues of animate beings. If they are, then it is not permissible to sell them until the head is removed, because trading in them is a promotion of and an aid to their depiction. Fatwas have been issued prohibiting the depiction of animate beings absolutely.

As for prayer, congregational prayer in the mosque is obligatory for whoever hears the adhan (definition) without loudspeakers. If one cannot hear the adhan except with loudspeakers, then he may pray in his place of business. It is better for them to designate a place where they can pray in congregation.