Re: The Stainless Steel Answer Station - ask all questions here - NOT FOR BUG REPORTS!
This kind of events affect some of your characters traits. For example, if you accept to do a donation for a great council, then your priests gain in piety. Regarding troubadour, s you mentioned, your princesses get more charm. That's useful if you want to marry a general from another faction. I'm not sure but it might also help for diplomacy.
I don't remember about pirates but I guess it works the same way.
To answer your last question, flying cows make your ennemy units sick, lowering down their stats. It works the same way on yours. So, take care when you use that.
Under the patronage of Flinn, proud patron of Jadli, from the Heresy Vault of the Imperial House of Hader