Get the modem/ISP issue resolved? Once resolved, then see if you still have the WIFI/connected issue.

Get a router (and modem) that exceeds your needs and does all you want. You will grow into it. Sometimes it pays to spend more and other times it is a waste. Modems are much like cars... Different...

The issue from the modem or ISP may be a contributing cause. Get that resolved, and then see if the WIFI has an issue. WIFI is generally slower than wired. The issue could be in your PC as it may...

Power off router, wait 30 sec, power on, and try again both the default and the custom userid/password. If still you can not get in, then you will need to reset the router back to factory specs. See...

Since the pc is connected to the modem, the issue is not in the router. Is it the modem or your ISP? Unplug the modem and wait 60 sec before plugging it back in. Wait a bit as it may signal the ISP...

1). If you needs are not great, either will do fine. I have a C8 with 17 wireless clients and 4 wired ones with a USB disk drive using 150 service and it is not anywhere near the limits. 2). Not sure...