Try to perform factory reset on your router. If won’t help - replace it.

Depending what region those “unofficial” are coming from. You could have problems if you need warranty repairs, or the phone may not support LTE/5G bands that are used in Georgia.

Linksys is fine, keep in mind there is V1 and V2 that are supported by openwrt, and apparently v3 is not supported. V1 got a bit better cpu. Also, if you can stretch your budget and want wifi6, check totolink x5000r on Ali express, time to time they appear on sale.

Under sensible configuration they can be OK. If look at it from vulnerability perspective, most of those devices are running Linux of some sort, so they all are vulnerable, unless updated frequently. A lot of vulnerabilities can be used to create backdoor, so it’s like one more or one less. But if you cut it off from internet and access it only from LAN or VPN, how those vulnerabilities will affect you? If there is opensoyrce firmware for it, like true storage or openwrt, that should cover you from built-in backdoors. I would only question hardware quality.