Does the Nexus 4 have 4G? I know it doesn't have LTE, but what about the 4G networks of other carriers?
If I happen to buy one, will I be able to use it T-Mobile's "4G" HSPA+ network?
Yes, it has HSPA+ which is what T-Mobile's "4G" actually stands for.

This article on AndroidAuthority should help you understanding  why it doesn't have LTE.