Do jews worship in churches?
No, Jews worship in synagogues.
Are Jews allowed to enter others' houses of worship for the purpose of engaging in religious services?
According to Jewish law, Jews are not allowed to participate in the worship practices of other religions. However, exceptions are made for houses of worship that fit with the rules for synagogues (no images of people, etc). As such, religious law allows for Jews to enter mosques but not churches. Even then, Jews are not allowed to participate in Muslim prayers, but can recite Jewish prayers.