Good price now (Cyber Monday) on this one, it’s popular and I see it recommended a lot:

GL.iNet GL-SFT1200 (Opal) Secure Travel WiFi Router – AC1200 Dual Band Gigabit Ethernet Wireless Internet | IPv6 USB 2.0 MU-MIMO DDR3 |128MB Ram

It has several modes, router is the regular mode. It can also receive your existing house Wi-Fi and repeater it, or generate wired ethernet output from It.

Tp-link makes something similar also.

Mine has a 24x7 call center, maybe yours does too

You might call your internet provider and have them test your line. Might not be your router.

Should be possible, multiple subnets will get you two different LANs. Good resource: Tom Lawrence youtube channels. He has an episode or 2 featuring VPN that should be helpful.

r/pfsense is also a resource that is available.

You can mount a conventional patch panel vertically (Monoprice 12-port Vertical Cat6 Mini Patch Panel, 110 Type (568A/B Compatible) (UL)

Or look at 10" patch panels for horizontal and use DIY rack panel mount strips ( like Cable Matters UL Listed Mini 8-Port Patch Panel with Mounting Bracket)

Try asking r/pfsense

Testers like Ideal VDV let you check it undisturbed in the wall. Use a patch cable that you verify known good first using the same tester. It will tell you if you have no choice but to re-terminate but won’t tell you which end requires re-termination.

Other similar testers from Klein or Fluke. Ideal can be bought at Home Depot in USA or elsewhere.