1. Can a fleet end its move in open sea? I can't find a rule forbidding it, but I can't image triers staying in open sea for whole season.
Yes - obviously they are beaching every night. The actions of Phormio and the Battle of Naupactus are a model here.
2. What's the difference between normal and spreading revolt? In either case you put a garrison in athenian-friendly city. Does spreading revolt allow you to put extra garrison in another city? I don't get it.
Spreading revolt allows placement of a a revolt in a region that has an existing revolt. See the sidebar on page 5 for the Regions.
3. How exactly does the plague event work? For example if you play plague on Athens do all units in a city lose 1 cv? What are non-cadres? Are there any units that don't suffer loses?
Cadres have just 1 CV, so non-cadres have 2+ CV. Each unit with more than 1 CV loses a CV. Garrison and Cadre units are immune.
4. Just to make sure on wintering moves: free moves are only to home city of a unit (for example spartan hoplites to Sparta). If it's not possible unit can move 1 area to controlled city or use action point to perform normal move?
There are 2 types of free moves;
Homing - which is a (forced) march or (forced) sail to a city that matches their colour (home city).
Quartering - which is a 1 area move to a friendly city. This can ripple in causing an unmoved and overstacked unit to move.(Displacement)
Units can also be ordered and move normally, for example a full (forced) movement to a friendly city.