Chance calculation help needed

For a balance check, I decided to calculate one little skirmish from start to end. Thus with some decision taking moments that will branch of in the tree with chances.

I don't know if I am calculating it correctly. Thus I need help with this. Just some back up calculations from the math people here is what I ask.

In my game:
A die roll means doing damage.
Rolling 1 or 2, means 0 damage.
Rolling 3 or 4, means 1 damage.
Rolling 5 or 6, means 2 damage.
The results of all the dice are added up.
Thus with 2 dice, I could get 0 to 4 damage, with 3 dice 0 to 6 damage etc.

For simplicity, I only ask to calculate 2 dice.

Situation A (99% certain that this is correct):
2 Dice are rolled. What are the chances to roll damage:
0? 1? 2? 3? and 4?

A chance out of 36
0 damage: 4 = 11,1%
1 damage: 8 = 22,2%
2 damage: 12 = 33,3%
3 damage: 8 = 22,2%
4 damage: 4 = 11,1%
Correct?

***

Situation B (absolutely (somehow) a question for me):
Again 2 dice are rolled. However, this time if you roll a 1(=0 damage) with one of the dice. You may reroll that die just 1 more time. If both dice, both roll a 1 (=0 total damage), both may reroll again.
When rolling 2, the damage is of course 0 and no reroll is allowed for that die.

Again the chances of getting damage:
0? 1? 2? 3? and 4?

I have currently 2 different solutions for situation B!
I know that the chance on 0 damage diminishes compared to situation A, but the total damage will never exceed 4.

0 damage: 7,4% or 4,9%
1 damage: 20,4% or 17,3%
2 damage: 33,3% or 32,4%
3 damage: 25,9% or 30,2%
4 damage: 13,0% or 15,1%

Which one is the one that I need?