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YES, there is a limit. TWC previously used to restrict the number of available addresses on their rented modem/router combo gateways at 10. Users could not modify that setting. Then about a year before the Spectrum takeover TWC ioncreased the number of addresses to 25, still locked. I believe that home internet user Terms & Conditions still include a LAN device limit, as well as prohibiting any servers accessible from outside the home LAN.
Your device fanout plan based on speeds (100 vs Gig) makes sense. Eight dynamic addresses should be enough to handle all your wired ethernet ports, I suspect your gateway somehow got set into bridging mode so it is expecting to see a full router on LAN port #1 and nothing else connnected to anyother LAN port. If that happens you won't have DHCP, NAT, DNS, or WiFi and devices connected to LAN 1 and LAN2 will fight over the single available LAN address.
If none of your wired Gigabit devices can see the internet or pull a valid DHCP LAN address on 192.168.1.x, then I would suspect a bad CAT-5e patch cord between modem LAN port 1 and the Gigabit LAN switch. Gigabit utilizes all eight leads in the cable, one broken or flipped pair can completely kill the link from the modem.
Post back with your findings and we'll help you work through the confusion.