Yes indeed, it does support 16GB RAM.
For the WiFi issue I'd first run the inbuilt Wireless Diagnostics. Option click on the WiFi symbol in the menu bar, what up/ down speeds are you getting in comparison to max theoretical? Does it achieve full speed thethered directly via ethernet? I did have a card go bad but it did it sporadically, but always when downloading bigger files. Restarting the router I guess has likely been tried.
For the SSD, how long has it been in place for? How full is it? Perhaps run Black Magic Speed test to see first what numbers are involved.
I tried to run the Wireless Diagnostics and it just pops up and then closes, it never actually runs. The thing I noticed is the picture I posted in the reply above, the WiFi MAC address is all zeros. That doesn't seem right, my MacBook Pro has an actual number there and from what I've seen in Google searches that address should come directly from the wireless card.
As far as our questions go, he does not achieve anywhere near full speed whether tethered or on the rare occasion that he connects to the WiFi. It's not even necessarily downloading files, it's slow to just load a web site. And yes, restarting the modem and the router has been tried multiple times but no other devices have trouble so it has to be this MacBook.
I do not know how long the SSD has been in place, we bought it refurbished in probably 2019 or 2020. It's 1 TB so I know it wasn't original hardware, I don't think they offered 1 TB in 2012, and it is a touch over half full.