As I understand it...
About depicting Mohammad... it's not in the Koran, it's a tradition (hadith literature). So it's not the word of God, as muslims see it. Mohammad did not want people to depict him, in fear of people worshipping him the Prophet (or something else), instead of Allah.
I'm not too familiar with how all muslims really view the hadiths and what importance they give them, but they are not the Koran. IMO they should, in time (at least), be ready to accept the Prophet satire.
A reason for why muslims can't ignore certain parts of the Koran btw ("and change their ways like christians"), is because it is supposed to be the exact message of Allah. It was written down exactly like it was said (via the angel Gabriel). This is why you got students reading or repeating the Koran in the original language, if you translate it you will change the word of Allah. Doesn't change the fact that there are translations though.