If I untap all my attackers, do they stay attacking?
This is answered in the magic comprehensive rules, rule 506.4, in particular 506.4b:


  506.4 A permanent is removed from combat if it leaves the battlefield, if its controller changes, if it phases out, if an effect specifically removes it from combat, if it's a planeswalker that's being attacked and stops being a planeswalker, or if it's an attacking or blocking creature that regenerates (see rule 701.12) or stops being a creature. A creature that's removed from combat stops being an attacking, blocking, blocked, and/or unblocked creature. A planeswalker that's removed from combat stops being attacked.
  
  ...
  
  506.4b Tapping or untapping a creature that's already been declared as an attacker or blocker doesn't remove it from combat and doesn't prevent its combat damage.


So the attacking creature is not removed from combat when it is untapped.