I have had issues with Time Warner too… and I know the staff I had the misfortune to interact with are right here in our beautiful San Diego. For the loss of productivity they caused me, I really, really wish they lose their jobs.
I have had similar problems. TW seems to assume that everyone is computer illiterate. I resorted to asking directly for a tech after running my own protocol sniffer on my interface to determine the problem. I finally got through to a real tech and it really helped.
For the network problem.. skipping all of the transcript.
What is the manufacture and model of the WiFi/router? Could you describe the connections (which item is connected to which other item). I suspect that “dumbrenter” is correct on DHCP.