Q: In Zark City, are pyramids that are removed from the board by the action Convert/Demolish permanently out of the game?

…If so, would one be able to eliminate opponents from the game?

A: No. Pyramids that are removed from the board for whatever reason go back into that player’s stash to be used again. Players can never be eliminated from the game. Hence the “Hatch” rule which brings players back if they have no pyramids in play.