Side note: Narkissos is absolutely right about the etymology: al-Ilah just means 'God' in Arabic (like ha-'Elohim in Hebrew, 'al-' and 'ha-' being the respective articles), and is related to semitic 'el: 'God', probably coming from the verbal root for 'power, strength' (Brown-Driver-Briggs)
Muslim teaching:
Muslims teach that Abraham was the first muslim (meaning one who practices Islam or 'submission' to God)
Until the time of Muhammad, the Arabs lived in a time of Jahiliya or 'ignorance' of God - they were pagans. Then Muhammad, 'seal of the prophets', is given the final revelation by God (the Qur'an) and leads his people on the right track of Islam by his example (the Sunna or path of the Prophet).
Academic teaching:
Before the rise of Muhammad, Allah was one of the pagan gods of the Arabs, who had three daughters (al-Lat, al-Uzza and al-Manat - see wikipedia on the Satanic Verses). Just like Yhwh some 1500 years before, Allah is upgraded from a polytheistic god (one of many gods) to a henotheistic god (multiple gods, only one, Allah, must be worshipped), and ultimately to a monotheistic god (the only existing god).
History sometimes repeats itself...
I hope this answers some of your questions,
Regards,
Deus Mauzzim
P.S so where Yhwh was probably borrowed from the canaanite pantheon (search wikipedia on Ugarit) and upgraded to the only existing god by the Jews, Allah was an indiginous pre-Islamic God who was upgraded by the Arabs themselves.
Of course, Muslims maintain Yhwh/Allah has always been one and the same god all along - because the Jews and Christians corrupted their scriptures and failed to totally surrender themselves to God, He found it necessary to try everything again with a different people (the Arabs). This argument is somewhat like the Christians used against the Jews.