Harry, should you wish to know more about Islam and their prophet, Muhammad, I would suggest a visit to
this page on my own website.
Yes, Muhammad did exist. He was born in 570 and died in 632. His life is well documented. As to whether the Angel Gabriel did speak to him, the Muslims certainly believe that is so. Muhammad himself was quite shocked by the first experience in which he claimed this happened, wondering if he was hearing a demon, or if the cave he was in at the time was haunted, and he was greatly troubled. But over time he claimed to have countless visitations and the Qur'an contains the revelations he believes that he received from Allah via Gabriel.
"Allah" is the word for "God" as used by both Christian and Jewish Arabs. When Christian Arabs are using that word, they are referring to our tri-une God known in the beginning as Yahweh. Same too, the Jews. Muslims deny so much of the character and nature of Yahweh that it is highly contentious that their Allah, being so different, is the same God as Yahweh. I am one who will argue that Allah is not Yahweh, having done considerable reading and thinking on the subject. However, the Roman Catholic Church takes a different position. Pope Benedict got himself into a great deal of hot water last year in his lecture at Regensburg when he dared to suggest that Islam's view of God was a misinterpretation of who He really is, and hinted an implication that if their interpretation was wrong, then another option was that it may not be the same God that we supposedly share. This would put him at odds with his own Catholic Church catechism, and he did not go quite that far... but none of this was lost on the Islamic clerics and the outrage that followed was something to behold. But that is probably going further than you want to go at present, given that you are asking the basic questions about these religions. My website contains a great many online resources for following up an interest in Islam, so I will leave you to go there or not as you choose.
Thanks in advance if any of these questions are answered by you. 
