NP Level

It does 2 things: allows for greater power of the main attack and allows for greater overcharge of the secondary effects.

If it's a 5* SERVANT, it gives you bragging rights (apparently) and, if you are F2P, you get the hidden passive of triggering whales.

Totally depends on the servant. For some, the additional effects are quite underwhelming (E.G. Tamamo and Waver) but others will get a huge boost to damage. Overcharge is another benefit, however.

It buffs the effects that aren't affected by overcharge, generally it means more damage, but if the NP doesn't do damage it can be other things.
Waver for example NP1 have a 30% defende down on enemys and NP2 it is 40% (post interlude). Tamamo gets a boost in her heal.
Also Archer Artoria benefits from being np2 because of her heal skill that has a demerit of -10% np gauge, so you can use it with 110% or more np gauge and still fire your NP
But generally is just the damage that gets boosted