The number of holes in the rim has to match the number of holes in the hub. Looks like the SON hub comes in most of the standard drillings, so you should be able to find a match. If you like your current rim, you can certainly have a new hub built into it. Seems like rims don't last as long as hubs, and they're not as expensive in general, so maybe you'll want a whole new wheel. But you might easily end up with a custom built wheel anyway, to get the hub and rim you want. Still, if you happen to find somebody selling the whole affair pre-built, maybe you'll get a better price.
I'm not an expert but I think you have lots of options, at least possibilities.
Not quite sure the considerations on rim width. Of course a rim the same (exterior) width as your current rim, that is sure to work. But no doubt you can tweak it wider or narrower a bit. The brakes would have to reach/clear the new width - I expect that's a matter of the spacers between the brake arm and the brake shoe. Plus the rim constrains the tire to some extent, so you want to make sure that there's a tire you can use that fits both the bike and the rim.
Ain't technology fun!