Would this also work if I'd given it vigilance before declaring the attack?
Untapping it does not remove it from combat[CR 506.4, CR 506.4b]. Neither does tapping it to pay a cost.
You get the chance to use abilities at the end of the Declare Blockers Step[CR 509.5]. The game will only advance to the next step once all of these has resolved and noone want to activate any others[CR 116.4].
Damage is only calculated in a later step (the Combat Damage Step)[CR 510.2], so the +1/+1 counters added in the Declare Blockers Step will affect the damage dealt.
Yes you can.
The combat phase consists of five steps:
- beginning of combat
- declare attackers
- declare blockers
- combat damage
- end of combat
In each of these steps players get priority and can cast instants or activate abilities. In the declare blockers step the first thing you do is declaring the blockers. It is after this that each player gets priority and can do stuff. And this is before the combat damage step