Good questions, and the first two are ones that scientists are still grappling with.
1) Probably both. Feathers evolved in a gradual progression, and we see different stages of them in different families. Here's a list...
- Spiny bristles: Tianyulong (a heterodontosaurid, which is a basal-ish ornithischian), Psittacosaurus (early ceratopsian, as you know)
- It's complicated: Kulindadromeus (ornithischian; I'll get to this later)
- Hair-like filaments: basal coelurosaurs, compsognathids, tyrannosauroids, therizinosaurs (possibly downy for the latter three)
- Downy feathers: ornithomimosaurs, alvarezsaurids, oviraptorosaurs, paravians (incl. dromies and trooies)
- Vaned feathers (usually as 'wings', sometimes as a tail fan, leg wings or head crests): oviraptorosaurs, paravians (incl. dromies and trooies), possibly ornithomimosaurs.
- Additionally, feathers regressed into scales occasionally; all known tyrannosaurid skin has been scaly. And, obviously, different parts of an animal can have different types of integument.
The theropod progression looks pretty simple - hair-like structures appear in coelurosaurs, and become gradually more complicated in each wave of their descendants. This leaves out coelophysoids, ceratosaurs, megalosaurs and allosauroids, unless a new find reveals evidence of feathers in them (though we don't have much evidence of scales either).
Ornithischian integument is trickier. We don't know whether their structures are related to the proto-feathers seen in theropods - if they are, then bristles must have been present even in the earliest dinosaurs. To add further weight to that theory, dinosaurs' close relatives the pterosaurs were all furry, and a few other archosaurs may have been too.
But getting back on point, ornithischians show a definite preference against any type of insulation - the
vast majority of their skin samples have been scaly, unlike theropods; this even includes juveniles of the fastest-growing (and therefore probably highest-metabolismed) families. Even Psittacosaurus' weird bristles would only have been for display - it's entirely possible that they evolved separately.
The real oddball is Kulindadromeus, and I'll get to that in #3.
2) Welp, looks like I've answered that. The earliest examples of feathers date back to the Late Jurassic. Interesting to note, the first trace of mammalian hair is only 15 million years earlier, but our ancestors from the earliest Triassic probably had it.
3) Okay, Kulindadromeus is a small Jurassic neornithischian, ancestral to ornithopods and hadrosaurs, and probably to marginocephalians (pachies/topsies). It will either go down in history as the watershed moment that we discovered feathers were a pervasive dinosaur trait, or a truly bizarre quirk of convergent evolution.
It has several types of integument. Firstly, scales in an unusual pattern, on its tail, feet and lower forelimbs. Second, hair-like feathers (similar to those found in basal coelurosaurs and compsognathids) over most of the rest of its body. Third, down-like feathers on its upper arms and legs. Finally, unique narrow bunches of fibre sparsely across parts of its leg.
What makes it
really weird is that it seems to show advanced feathers which hadn't developed in early coelurosaurs. Surely that, at least, has to be convergent evolution. Curiously, no trace of the bristles we see in those two other ornithischians.
Anyway, hope that's been of some help.
:edit: All that trouble, and it turns out there was a much simpler chart online I could have used. Here it is (it's missing quite a few groups though, my list's still more comprehensive...).
