> Does this require node.js as a server?

Yes

> How does the page-based router deal with routes like /things/123/subthings/456?

It doesn't, you have to use the programmatic router for that.

> Typescript?

Don't believe so, see this comment in this thread: https://news.ycombinator.com/item?id=13968723

There is a typescript example on their page:

https://github.com/zeit/next.js/tree/master/examples/with-ty...