Yes they are Semitic words, but they are pronounced differently depending where you came from. That does not mean Christ said Allah or that he meant an Islamic god.
There is either One God or there isn't. There is no such thing as "an Islamic god" any more than there is "a Jewish god" or "a Christian god". Such relativist language subverts the very concept of monotheism.
Yes, but even in the modern Arabic you pronounce the words differently, depending on which country you are from. So the Arab from Algeria might need to right the words down in order to be understood by Arab from Iraq.
In Semitic languages vowels are especially fluid, the consonants tend to be more stable and usually they are written down.