Is it possible to render video inside animation, for example import avi file in to TV box like a skin or texture for kineskope (monitor) or how to show avi in modeled TV during render?
Yes, just add the AVI as an image texture to the TV screen material.
You may not get the sound from the AVI, however. You may have to use the video sequencer to get the sound.
Good to know. Does this by any chance work with animated GIFs too?
yep, any image sequence works as well, so even a folder of j(numbered) pgs or pngs.
when loading an image texture, look for an option labeled “movie” or “sequence”