The current tram system takes up a lot of surface space, that would be more well used for other things.
Also metros are cool
How?
Simple build a couple of metro stations and connect them with tunnels. We can also move some water elevators to the metro stations which will make the surface (especially blair mountain str) look much nicer.
Good idea, but currently the city is so tiny that it'd take more time getting into the metro and going places than just sprinting or flying. Although if you could figure out how to make stations work that would definitely be great.
I would cut out Revolution Square and just connect Castro Square, Blair Mountain Street, Lenin/Trotsky Street, and People's Council. Everything else you suggest is literally like a 30 second walk. Actually my suggestion may be impractically close as well.
For Blair Mountain Street Station, extend it towards Revolution Square to access the mausoleum and mines.
How deep does the metro go? According to your layout, the 'beach mine' might come in the way between Revolution square and Blair mountain street. There is also a 'machine testing lab' near Lenin Street, but I don't remember where exactly. Otherwise I think this could be expanded. From Castro square stop a path could go to the Iron farm and from Lenin street to the new storage house. What kind of metro system are you building transporting-wise? Ice boat, piston bolt or a mix of both?
Those thing shouldn't be a problem, the beach mine will be below it anyways and going thru it isn't a problem either. The machine room will be moved a bit, but there is not much in there yet so it will be a small amount of work to move it.