Are “Cerveja” and “Service” etymologically related?

Answer 1

No. In spite of the somewhat similar sound if you are an English native speaker, the word "cerveja (beer)" has it origins in the name of the Greek goddess "Ceres," the goddess of grains and cereal. Beer is brewed mostly by grains like barley. "Service" comes from Latin servitium ‘slavery’, servus ‘slave’.