How should I retouch videos (repaint areas)? Let's say I have video on some frames of which I have some objects that I would like to cover up.
I would put video on plane as texture and put some objects in 3D scene before this plane and move them accordingly to video.
How exactly to do it ?
I'm able to put video on plane, but don't know how to make it play and save sequence into file, also I would like to use motion tracking.
First of all:.

I do strongly suggest to not put the video as texture on a plane in 3D-space. If you wanna use video input, it's objectivly better to use the sequence editor of blender, where you can add your videos and overlay them with renderings.

Second:

I think you kinda overestimate the ambition of this stack exchange community, because explaining how to do this task is probably more complicated than doing it. I don't think you will get a fully-featured tutorial on how to do this as answer, cause it's just too much work.

There are, however already tutorials how to do this already online. I suggest the following guide: https://www.youtube.com/watch?v=CVPcT0dJmoY