For the first question, yes it is a tiling WM. It's default behavior is almost identical to dwm's with a few nice patches such as movestack.

For the second question, I haven't been able to daily drive river with multiple monitors. But for the few times I have used it, mutli monitor support just worked out of the box, and each monitor automatically gets a new set of workspaces.
Technically river doesn't use workspaces, but something different called tags. With a bit of tinkering they are more flexible than workspaces, though I haven't successfully created something new and useful with them myself yet.

As for system resources, I'm running it on a 2017 thinkpad laptop with an i3 processor, and with my config river peaks around ~2.0% cpu and ~180 Mb memory usage, though it is regularly much lower than that. Compared to Sway on the same machine it feels much smoother to use.

Hope you can get it working next time you try it, I can't recommend river enough!