Can I tap a card after I assign it to block?
During the combat phase, after I assign a blocker, can I then tap that blocker for its activated ability?


Yes.  Blockers only need to be untapped when they're actually declared as blockers; after that, tapping &amp; untapping have no effect on blocking or any other parts of combat.


  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.





  What would happen?


The activated ability would go on the stack, like normal.


  For example, say that a 1/1 Saproling token equipped with Healer's Headress is assigned to block an attacking 3/1 Blade of the Sixth Pride, but after it's assigned, the Saproling is tapped to prevent one damage to it. Is that legal?


Yes.


  Would anything change if the attacking creature had first strike, like Ambush Party?


No.