I'm a Sophon 54 turns in and It is nearly all going... to what? Is that it automatically filling my ships? If so, it should say.

Also, if I know that my fleet might perish in a fight above one of my own systems, is there any way to "evacuate" its manpower beforehand?

Lastly, my guardian ship which could carry manpower and siege equipment is also programmed to try to get fired on! Is there any way to change individual ship class behavior?

Popup explains it, it is used to populate ship crew (ship with crew gets up to 20% bonus damage), ground troops for system defence, and when all is filled it is directed to empire reserves until cap is reached.

No way to "evacuate" it manually beforehand, but there is combat tactic (i think it is called "Life pods away"?) that allows you to evacuate (portion?) of crew into empire manpower reserve upon ship destruction.

I'm not sure I undertand last question right, what is "guardian" ship? Are asking, if coordinator and protector classes can lower their target priority? Well, for the most part it depends on attacking ship, but there are modules that allow to lower target weight of individual ships.

Targeting modules explained 

Unfortunately, this means you are trading siege and manpower modules for target weight modules.

If you afraid your seige ships to be destroyed, I'd recommend to create separate protector/coordinator designs for combat (equiped with support modules to tank as much damage as they can) and for siege (equipped with siege modules), then distribute them into forward battle fleet, and rear siege fleet. First you send a fleet to clear all danger, then the second to lay a siege.

as for the guardian ship.

That behavior is tied to the hull you selected.

If you want a siege ship that will be targeted less often, use a different hull as the base.

Yes this will have fewer useful slots for that design. It is a balancing act.

Or, keep all of your siege ships in a second fleet and make sure it never has to fight.