You could go over a wired network.

You want a switch, not a splitter.

A splitter is for running two 100 Mbps connections over a single 4 pair cable, and it uses splitters at both ends of the cable.

That is correct, yes.

You could setup a steam cache/LAN cache server so you only have to download games and updates once though.

You’d want iSCSI, but everyone gets their own volume to avoid issues like that.

Unless you get a desktop replacement laptop with a entry level CPU, then it’s still going to be thermally limited.

If it says i9-12900KS, then that’s what it is. There isn’t a difference, they’re the same thing.