Answers to your thoughts:
You will have to hand write your own custom rules for PVP situations, as PVP actually flies in the face of the game design. One of the core conceits of the game is that only one person should roll in any given action, and that it should almost always be the player.
I don’t feel that would be a good idea, since almost all of the cyphers have a level that is variable. Two cyphers of similar level have a similar effect, but one takes up more space in your “cypher slots” sounds like something potential players would complain about in the long run. If the staff is doing their diligence to create situations where cypher turnover is happening regularly, there’s no need to put further constraints on number of cyphers owned / used.
Nope. Artifacts are not cyphers, so they should factor into that. That said, Artifacts are meant to be rare, so again, if staff is doing their diligence on that, you don’t have to worry about a lot of them existing, especially if you use plot to write them out of the story. (That big laser gun artifact you found is actually the power supply for this one thing over here, and when you install it, you can’t get it back. Sorry.)
Also nope. See staff doing a responsible job of controlling the flow of these things into the game. (Also if it’s basically the Numenera equivalent of a Ford Focus, do we really care if there are bunch of them?)