New CM1200 - self-assigned IP address via Ethernet Connected Laptop - NO Internet

> [...] I think the solution is to not connect additional devices to
> the CM1200.

   One might get that impression from reading this thread.

>    Connect (only) your router to your modem. [...]

   Which part of that was unclear?

> My Netgear AX1800 only has 1 LAN port [...]

   What is it?  "AX1800" is a speed, not a model number.  Look for
"Model" on the product label.

> [...] do I then need an AP after it to allow mutliple wired
> connections from the router?

   "the router"?  Have you a router?  Has it a maker and a model number?
Care to share?

   An "AP" normally means an "access point", which is an abbreviation of
a "wireless access point".  Not normally required to add "wired
connections from" anything, but typically could be used that way.

> What is a NAT router?

   A router which does NAT.  (Is Google broken?)

      https://en.wikipedia.org/wiki/Network_address_translation

   Practically any router which you'd be likely to buy would do NAT.

   You might want to start your own, new thread, for your own, different
problem(s).  Include an accurate, useful description of your devices,
and of what's connected to what.  (Hint: If a device has different types
of Ethernet ports, then "connected to device" is not enough detail.)

   What you're actually trying to do might be interesting, too.