create a fixed height and width for profile photos
Kind of.  They currently aren't technically true "Assets" like in the rest of Craft.

The most you can do is pass in a size to the method getPhotoUrl(45) and you'll get a 45 x 45 square result back.  I believe it will crop from the center only.

We have plans for Craft 3 so they'll be treated like 1st class Assets and you'll be able to perform transforms on them like any other Asset.