Islam recognizes the Jewish, Christian, and Sikh God as the same. The name Allah is a different name for Yawweh. Most serious religious scholars (mostly priests) are of the same opinion:
"The Church regards with esteem also the Muslims. They adore the one God, living and subsisting in Himself; merciful and all-powerful, the Creator of heaven and earth, who has spoken to men."
You are correct! Muslims who cannot treat Mohammed as a human are breaking one of the chief tenets of Islam. You are allowed to picture Mohammed as you wish, just not Allah. The idea is that a picture/drawing/depiction would allegedly cause worship . . . except Muslims who scream about his (Mohammed's) depiction essentially idolize him.