How does PvP gear work?

PvE player here, I’ve been trying out PvP mostly to get a few of the transmog sets and I’m very confused about how gearing works. I’ve been playing RBG to get honor to be able to buy the Aspirant PvP gear, which from what I’ve read I can then use to play Rated to get conquest to get the Gladiator gear?

How does tier set play into this? I’ve read tier set exists and is important for PvP, but I can’t figure out how to get it. Should I be using the catalyst for it? I can’t unlock PvP vault until I start doing rated, but I’ve read I shouldn’t do rated until I have PvP gear, but it seems like I shouldn’t give up my PvE (HC/Myth) 4p set until I have an equivalent in PvP. But I can’t figure out how to get it in PvP.

Also, what is the difference between PvP and PvE gear? The PvP gear says in the tooltip that it scales up in PvP content so does that mean PvE gear scales down in PvP content?

How does upgrading work? I read that PvP gear can be upgraded with honor, but I can’t figure out where to do that. I also read it can be upgraded with flightstones/crests for world and non-PvP content. The tooltip for the gear says “”1/8 Explorer” and “1/8 Champion” - does that mean for world content or for PvP content?