Y Singh, 1. Mohammed himself told his followers to convert infidels = non-Muslims to Islam, if they refused, to kill them with swords. (Source: Hadiths)
2. The Quran states that Namaz shouldn't be done by a man in an intoxicated state, or when he is just back from a journey or even when he has just touched a woman. If he has just touched a woman, he is supposed to smear dust on his forehead and then perform the namaz. Implication: Women are dirtier than dirt.
3. Quran says that all Muslims live and die for Allah. Mullahs are the intermediaries between Muslims and Allah, hence, Muslims follow whatever the Mullahs say.
4. Yes, since a Muslim isn't supposed to convert to another religion.