High 50s is perfectly fine. Obviously bumping to about 70 during shed.
Your snake may still be working the rest off, let him do his thing. Ideally, yes it'll come off all in one piece, but not always.
The areas you want to focus on most are actually eye caps and tail tip. I always check the cloaca too. Eye caps you already know about. Tail tip is very important too. Head, not so much. Of course, you want the head clear too, but there aren't direct health concerns like tail tip and eye caps.