Is it permissible to wear something bearing the Star of David, and is prayer valid with such attire?

A Muslim is not permitted to wear or use items bearing the symbols of the enemies of Allah, such as Jews and Christians. Whoever does so out of love and loyalty towards them apostatizes from the religion. If done for any other reason, it is forbidden. As for performing Salah while wearing such items, the majority of scholars consider the Salah to be valid. The Star of David is a symbol of the Jews and of evil, and a Muslim is not permitted to use it.