1) Is Rails still the best choice for a PIM-like web-based system? 2) Is Rails still popular and the defacto standard of the Ruby community? 3) What's the current best practice for running production? Passenger + Nginx?
It's still the best choice in the Ruby world, well maintained, responsive and new features added. Shopify and github use it, you might want to look at the Rails 6 annoucements what these companies added for scalability features. There've been changes to the asset pipeline since version 3 but you'll still recognize it. You can run Rails as API-only and there's subprojects/tutorials for combining a frontend-heavy React,Vue with a Rails backend. You can still ignore the webpack based asset setup unless you use React,Vue I think. Ruby-3 works fine though I'm still waiting for some less-maintained gems to finally merge PRs, maybe you want to use Ruby-2.7 first.
I use https://puma.io/ , that scales well enough for me. https://github.com/socketry/falcon#readme is faster with build-in HTTP/2 support but harder to setup in my opinion, e.g. requires SSL certificate even on localhost.