Yes, they do now.
Once upon a Time they didn't.
There were even unique items that were a weird level. Adrointness (old bloodthorn touch) had a staff that only dropped at level 45 iirc.
Yes, as of One Tamriel patch (October 2016). Before that all sets had a different cap they stopped scaling, depending on zone or dungeon. For example Burning Spellweave did drop in CoA 2 before that, but it was VR14 (CP140) so nobody was using it since you could craft Julianos at CP160.