I've been reading through the documentation, but I'm not sure if the following two things are possible with MT:

permalinks of the form /yyyy/mm/dd/name_of_entry/ (individual archive pages)

archiving by category and date: /category/yyyy/mm/

I'll keep looking and post an answer if I find it, but if somebody knows, let me know!

It's right here, under Archive File Templates.

Archiving by Category and Date would only be possible with the Individual Archives, as Category Archives do not have a date context, and Date-Based Archives contain multiple entries (and therefore, have no single category to reference).

The method described in this thread seems to be doing what I want, at least for the archive by date and category part.