If you have not done a factory reset, do it. If that did not fix the issue, then the sensor or firmware is messed up and not worth fixing. If it is that cheap, get a new one. Since you have this experience, getting the exact same model could have the same issue later on.

You do not need another router. If you run a cable straight to you, you can then plug in an access point.

That is possible but why? You will have too much latency with this setup .

You can also add an AP connected to the switch for wireless devices like phones and also for laptops if you are moving around with it.

change out the switch to a 10/100/1000 so can get faster speeds. POE is nice if you plan on using APs or Security cameras that has POE. You are lucky that the runs are actually for networking and not for phone lines.