I saw the Ariane 6 animation, and I noticed, that the upper stage spins before deploying the satellites. Why are they doing this? Is it necessary or is it possible to successfully deploy a satellite to orbit without spinning it? Are the satellites spinning throughout their mission or they will stop spinning after reaching their desired orbit?
It's a stabilization technique. I'm not sure what you mean by "is it necessary"...they don't do things "just because" in rocketry. It's an alternative to three-axis stabilization.
The satellites are usually despun after the burn(s), often by the amusingly named "yo-yo de-spin". (good animation at link)