Let's say I want to make a character (an animal) with a stick in its mouth.
I dont understand if the animation (done in Blender) should have the stick in its mouth or if it should be done in Unity.
Is there any place where I can read the theory behind it? How shall I do interaction between two objects like an animal eating something?
It depends on what you're trying to achieve. In general I would try to do everything in external tool (i.e. Blender), because you need to duplicate imported animation in Unity if you want to modify it in Animation Editor.
But the basic idea with interacting object should be something like this: let's say you want to make character pick up weapon action, so you do the following:
1) you have two separate objects/models: character and weapon
2) you need a bone on character where you can attach a weapon; for character it can be a hand, or you can make a special-dummy bone for that
3) you need pickup animation
1) You place charater and weapon in the world
2) Play pickup animation
3) At "pick up time" parent weapon to the special bone/hand of the character
I hope that helps.