Can´t upgrade spymasters

Yes to reach level 3 they need to kill another spymaster. You can look up the specifics in a bunch of places but the gist is you need to put a spymaster in a different chain (just attached to your entrance is fine) then they’ll cause it to destabilize and level up. If you have spare locks you can lock the sacrifical spymaster and they’ll ‘kill’ it and level but not actually destroy the room (so you can level multiple spymasters consecutively without needing to get lucky finding more).

Don’t they upgrade by killing the spymasters at the end of your snake?

You really should watch some youtube videos about the temple mate otherwise you will screwup something later. Spymasters upgrade by killing other spymasters, also having a lvl 1/2 spymaster towards the end of the chain increases the odds of getting another spymaster which speeds up your progress

Medallion will only upgrade a room once. You need to have a spymaster at the end of your chain for it to be assassinated by another spymaster in your chain. You can lock it before closing the temple so the easy thing to do is open the temple, enter the temple, come out and then lock the last spymaster. You can have an additional medallion spot this way.

It’s not too late to turn back and do it the kgb way. I had a full no tech temple and I gotta say it was lack luster. Currently building a fub temple.