"No, Allah does not mean god. Arabic for god is ilah. (Read the shahada.)"
No, arabic uses a different alphabet to english, so that isn't the arabic for anything.
The word you've rendered as "ilah" means "god" (small 'g'), just as similarly "ilahah" means goddess. "Allah" is "God" (big 'g'), the name/title of their diety. In sura 14 of the Koran, Allah says the following...
Allah, unto Whom belongeth whatsoever is in the heavens and whatsoever is in the earth. and woe unto the disbelievers from an awful doom. [...] We verily sent Moses with Our revelations, saying: Bring thy people forth from darkness unto light. And remind them of the days of Allah. Lo! therein are revelations for each steadfast, thankful (heart). And (remind them) how Moses said unto his people: Remember Allah's favour unto you when He delivered you from Pharaoh's folk who were afflicting you with dreadful torment, and were slaying your sons and sparing your women; that was a tremendous trial from your Lord. And when your Lord proclaimed: If ye give thanks, I will give you more; but if ye are thankless, lo! My punishment is dire. And Moses said: Though ye and all who are in the earth prove thankless, lo! Allah verily is Absolute, Owner of Praise. Hath not the history of those before you reached you: the folk of Noah, and (the tribes of) A'ad and Thamud, and those after them ? None save Allah knoweth them. Their messengers came unto them with clear proofs, but they thrust their hands into their mouths, and said: Lo! we disbelieve in that wherewith ye have been sent, and lo! we are in grave doubt concerning that to which ye call us. Their messengers said: Can there be doubt concerning Allah, the Creator of the heavens and the earth ? He calleth you that He may forgive you your sins and reprieve you unto an appointed term. They said: Ye are but mortals like us, who would fain turn us away from what our fathers used to worship. Then bring some clear warrant. [...] And when Abraham said: My Lord! Make safe this territory, and preserve me and my sons from serving idols. My Lord! Lo! they have led many of mankind astray. But whoso followeth me, he verily is of me. And whoso disobeyeth me - Still Thou art Forgiving, Merciful. Our Lord! Lo! I have settled some of my posterity in an uncultivable valley near unto Thy holy House, our Lord! that they may establish proper worship; so incline some hearts of men that they may yearn toward them, and provide Thou them with fruits in order that they may be thankful. Our Lord! Lo! Thou knowest that which we hide and that which we proclaim. Nothing in the earth or in the heaven is hidden from Allah. Praise be to Allah Who hath given me, in my old age, Ishmael and Isaac! Lo! my Lord is indeed the Hearer of Prayer.
Abraham, Moses, Noah..? I can't help feeling I've heard those names somewhere before!
