Some Muslims do kill people, sometimes for the same reason as anyone kills a person and sometimes for their religion, but not all Muslims kill people. Moslem terrorists are trained to kill the infadels. All those who are not moslems, mainly Jews and Christians. They want all who are not moslems dead. The radical terrorists have twisted the religion of Islam. Mainstream moslems are peace loving.
Arabic and Islamic are two different things. Arabic refers to a language spoke by Arab people and some non Arab moslem people. Islam is the religion whose sacred book is revealed to the prophet in Arabic Language. Islamic is an adjective given to things (and not to persons) such as Islamic Art. Moslem is the adjective given to a person whose religion is Isalm.
Formally speaking, there were no Moslems until Mohammed came and preached the Religion of Islam. However, the term moslem (with a lower-case "m") refers to somebody in submission to the Will of God, but not accordance to the exact dictates of the Religion of Islam. Moses, being one of the Prophets of Islam, was certainly a moslem, but could not have been a Moslem because the Qur'an had not yet been revealed.
Moslem POV: According to the Qu'ran, Islam was around long before Mohammed showed up, and Adam is noted as one of Islam's prophets. While I don't recall Eve being specifically mentioned, it seems likely she was at least Moslem. Other religion's POV: Other religions that takes the Old Testament or Torah into account clearly don't assume Adam and Eve were Moslem.