Use CAT5E or CAT6A and buy some keystone jacks for easy installation. For the switch, buy a unmanaged Gigabit switch with at least 2 more ports then you need for future proofing.

Modems MODulate and DEModulate.

If it has Wifi, it’s not a modem but a modem/router combo(AKA gateway). What model is it and the router your thinking of?

What do you have as a router now? Sure you need a router and not a Access Point? Those are cheaper.

The levels look good although you are missing some downstream and upstream channels. Should be 32x4 at least. Do the signal levels change when you move the modem? Also, what part are you moving? Sounds like a broken coaxial port on the modem to me or something like that.

Signal levels?

ISP usually charge for extra IPs as IP addresses are limited. Wouldn’t affect your data/speed though. If you want multiple IPs look into business internet. For confirmation, who is the ISP?