Here are the important variables for performance:
In all, 300 to 500 is what I’d expect with modern gear in a typical household. You may be able to consistently get more if you are in a radio-quiet area or very near the router.
Yes, you can create new networks and just ignore the existing wiring. You might want to uplink to the provided service. Lots of options.
I’d likely get a fully programmable and manageable router and switch and AP and start with that. Maybe get one of those little racks.
Have fun.
I’d install a cable (or have a cable installed). There is no substitute for a cable.
Another option is to repurpose (quality) Cat5 based telephone cables for Ethernet, or reuse legacy cable tv wiring (“MoCA”)
Basement or utility room seems like the perfect place for the modem. I’d run Ethernet up from the basement into the living space.
I’d spend about $200 for a switch and AP and wired router. Spend the balance on proper Ethernet wiring.
Possibly due to a weakening power adapter on the router, not delivering enough amps. The PC connection makes the CPU or radio get busy, but a lack of available power leads to a hardware crash and self-reboot.
I’ve seen this many times.
It may be worth trying a compatible replacement power adapter.
Band steering isn’t something I’d consider in a typical home network. I do enough admin work at work.
Hopefully those coax cables make no turns, because otherwise your pulls will be get bound up. Coax is stiff and will fight you every inch of the way.
Bad cable.
It is impossible to know if this is Ethernet via the photos. “RJ45” style jacks are used for numerous applications.