Is there a roster limit prior to training camp? IE will I have the computer auto-cut anyone if I go over 60 from FA and then the draft? Also, is there any way to set a cut order to ensure none of my starters get axed instead of camp fodder?

I believe so, you can sign no more than 60 or the CPU will cut your roster for you to 60.

This is correct. You can have more than 60 during the free agency stages but you must have your roster cut down to 60 for the TC stage.