I've made a simple animation which moves an object along one axis back and forth. Now i want to change position of this object, to fit the rest of the model - but after playing animation, it goes back into place that it was previously animated. Is it possible to animate in local space? (to be able to change global position of animated object, and keyframes will not overwrite it)
Yes, but a much simpler (conventional) way is to have a setup like this.
Empty2 -> Empty1 -> Object, where the arrow represents a 'parent of' relationship.
The Empty2 is a parent of Empty1, and Empty 1 is a parent of Object. Then when you keyframe Empty1, Object will move accordingly. On top of that you can then keyframe Empty2 and Empty1 (and therefor Object) will move in relative orientations.