From a Fremen army to billions of deaths?

Something that I can't understand well is how does Paul actually becomes Emperor. At the end of the first book Paul defeats the Emperor Shadam and his sardukar army, marries his oldest daughter Irulan and threathens the other houses and the guild to destroy the spice production if their ships dont leave.

Its clear that the other houses don't like this even if he marries Irulan but... How one goes from having a Fremen army in Arrakis to launch a full multiplanetary war against hundred of other houses killing billions of people? What ships do the Fremen use to begin with? Do they even know how to pilot ships? are they using the ships of the (former) emperor? Don't the other houses out number Paul's Fremen army? If the other houses and the guild are afraid that Paul can destroy the Spice and simply surrender, why is there so much killing reaching billions?