Your answer is neatly found in the Example on p210 of the DFPRG Volume One: Your Story book.
I'm not positive how much I could quote from the non-SRD document, so I'll instead paraphrase:
- The PC's establish a thaumaturgical Block (shield) with a Fantastic (+6 strength)
- The enemy makes an Attack with a gun (weapon:2) and rolls an Epic (+7) on their shot
- The targeted PC has their block of +6 and rolls Athletics to avoid the attack altogether, but only gets a Good (+3)
The result is that the PC is struck for 3 stress (7 Attack - 6 Block + 2 Weapon). Without the Block, she would have had to deal with 6 stress (7 - 3 Atheletics + 2).
From this we can answer your questions:
If the target character let the block absorb the attack (b), does the Block receives the full attack strength (3 + weapon:2 = 5), which would be enough to surpass (and kill) the block?
Your Block is compared to the Attack before the weapon, so the Attack would not be successful in your example.
However, if the character tries to avoid the attack, it rolls against only the attack value (not weapon). But when she fails (3 - 2 = 1), does the Block still receives the remaining strength (1 + weapon:2 = 3) or the Block is ignored (considering the character leaves the block protection)?
If you do not roll more on your Contested defensive roll, the Block takes the full brunt of the Attack. You do not add the Block to your Contested roll (which is what comparing the remainder would be, in essence) but instead the Attack is compared to 'first one then the other' or functionally the greater of the two values.
If the same character directly attacks a Ward. Does the Ward also receives the full attack strength (3 + weapon:2 = 5)?
Wards are functionally Blocks, just with the added ability to reflect attacks that do not defeat them. You would compare the roll of a 3 against the Ward, and the attack would fail, causing the attacker to have to roll against a 3 shift Attack at them. Somewhat incongruously, Wards don't seem to reflect Weapon ratings.
For reference, the actual wording on Block:
During the exchange, any time a character wants to perform the action
that’s covered by the block, he must roll against the block and meet or exceed the block strength to be able to perform that action.
A weapon can inflict additional stress on a target when you succeed on an attack and, likewise, armor can mitigate stress. Weapons and armor are given numerical ratings, usually from 1 to 4. Any successful attack adds the weapon value to the stress inflicted, but subtracts any relevant armor value. Keep in mind that a tie on an attack roll does connect—if you have a weapon rating,
you would add the rating to the zero-shift attack for a final stress total.
As you can see, Weapon ratings are not applies to Attack rolls unless they are at least equal to the defensive roll/Block.
Finally, the wording for Wards' reflection:
When something hits the ward, compare the shift values. If the ward prevails, hit the attacker with an effect of the appropriate type
for equal shifts. So if someone rolls a Great (+4) attack against a ward, he has to try to avoid a Great (+4) attack from the rebounding force. If
someone hits it with a 6-shift evocation, he has to dodge a 6-shift evocation.