Mismatched rims, and tires that may be too wide?
The thing that confuses people about all the newfangled inner rim width to tire width compatibility charts is that while the effect they're trying to steer you away from is real, it's not binary. It gets more squirrelly, floppy, and prone to blowing off the narrower you go. The point where there are major issues in practice depends on rider weight, inflation pressure, riding style, the fit of the tires, and other factors.
A 2.1 on a 16mm inner width rim is somewhat extreme by rational standards, but when rims like that were trendy there were a lot of bikes running around with such a combination. It will probably be fine, but it's on you to decide whether you want the risk, and how reasonable it is depends completely on your application.
Transplanting the hub makes sense as wheelbuilding practice if that's what you want and if the rim and hub in question are in good condition. That kind of job makes little sense from a time/money perspective if all you want is a functional bike, but it's also how skills are built. Use new spokes and nipples.
There are many times when using a rim that narrow creates some hoops to jump through when setting up the brakes on a frame that predates the trendiness of super narrow 26&quot; rims. Eighties and early nineties MTB frames often had rims and post spacing that were about as wide as they should have been. Brake and pad models differ in their ability to get the pads in so far. That in practice is a thing you need to try and see.