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If a squad is partially under the shield and partially outside, does it count as being protected against enemy shooting if models outside the shield are closer to an enemy?

Yes.
In fact the way the core rules work it MUST apply to whole units, it can't work in models.

The PVS shield applies to targets. Targets are always units, never models. If you look at the rules for measuring, it's closest point to closest point. So if one model is in range the whole unit is.

What is PVS shield?

And about 2nd and 3rd layer of shield: if an opponent shoots away 1st layer, then he has to deal with 2nd and then with 3rd and only after that damage is done to models, right?

Projected Void Shield.
The rule that the Void Shield Generators use.

VSG is the building, PVS is the shield that covers units.

Never thought to play it that way before, but yes, that's what the rules say!