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I have a question about this before I buy. So my question is, if I import my map into UE4, will I be able to edit the textures on individual sides of a model like in Hammer?

Not at the moment, I'm afraid. If it's a single brush, you can export the fbx to your favourite editing program and re-import. If it's multiple brushes, you should be able to tell HammUEr to only reimport those after you've modified them in Hammer.

(Epic are working on some kind of in-editor mesh modification thing, tho, although I've only seen it demo'd with VR?)

Ok. However, If I do use textures on different faces will it also be transferred over to UE4?

I'm assuming you mean "can a brush have multiple textures on it and still keep them", right?
Then the answer is yes. The materials you've selected in Hammer will be applied to the faces in UE

Yes, that is what I mean. And thanks for the reply!