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[The Fifth Horseman]

1. When Duke Leto heard that a sietch had been taken over by the Harkonnen, yelled and said that he has to go on a mission he may not come back from and simply vanished from the storyline.

IIRC Jessica mentions his death later.

3. When that annoying Shaddam couldn't leave me alone and just wanted more and more spice.

Mine out the first bunch of territories before you go to the desert and start having visions. The plot won't progress, the Emperor won't demand any Spice for a while and you'll have plenty of time to prepare to leap onto the new territories you find after that.