The cabling in your wall is, for all intents and purposes, never going to be messed with again and lives in a place that isn’t accessible. Ignoring any fire or heat related considerations, aluminum and copper expand and contract at different rates. Eventually that cable will fail as the heat from the extra power for PoE will cause deterioration. You’ll just replace the patch cable at the end when that happens, but the main run is a much bigger deal to replace. Don’t save a dollar now to spend it many times over later.

You need to reset and reconfigure the extender. Using the same password and SSID isn’t enough since there’s a unique ID in play as well, on the router end. That changed.

I’ve been down this path before. I made my old DS3615xs be my plex server and do 4k transcoding after upgrading the CPU. I now run it on an i7 NUC with hardware transcoding capabilities. Decoupling the plex server from the storage allowed for independent upgrades, and I could switch over to my backup NAS when I had to do prolonged maintenance on the primary. It was cheaper overall too.

The PCIe spec says you should be anyhow

It’ll only run as if it was in a 4x PCIe 2.0 slot, so 2000MB/s.

In the list of things you’re asking for, monitoring searches is going to be impossible (it will involve breaking SSL or attacking the network in a way that will be extremely obvious to the client), monitoring or blocking site access is trivial to bypass, but it is easy to rate limit for bandwidth. Rate limiting is probably built into their existing router, as it’s a very common feature, so they just need a router new enough from a manufacturer that has a phone app.

The other things sound overbearing and not very becoming of a host family. Monitoring web searches? Really?

There are lots and lots of 24 port gig switches, fanless, and not PoE. HP ProCurves are cheap and good entry devices. If you don’t have a big need for PoE then get an 8 port fanless and connect the two.