If a skirmisher with fatigue equal to his stammina makes an attack and rolls a surge:

1. He may lost immediately a fatigue, so he can get this fatigue back to use "Deep Wounds" on the same attack?

2. He lost the fatigue after the attack so he can not get a fatigue to use "Deep Wounds" on the same attack?

1 is the correct answer

cf CRRG p6 last point on "Spend surges" ( https://community.fantasyflightgames.com/topic/242877-community-rules-reference-guide-crrg/?page=1)

More globaly, unless stated otherwise (like for conditions, ...) surges effects apply immediately.

Surges can be spend to recover 1 fatigue only in step 4 (Spend surges) of an attack. The fatigue is recovered immediately (and could be used to trigger another surge ability in this step). Any surges rolled that are not spent in this step of the attack are lost.

Deep Wounds' triggering condition is "when you resolve an attack". An attack is resolved in step 5 (Deal damage) after damage is suffered. My interpretation is that Deep Wounds may be used immediately after an attack is resolved but is not part of step 5 itself. Thus, if the Skirmisher is able to spend a fatigue immediately after resolving an attack, he/she may use Deep Wounds. Note that Deep Wounds only affects one figure that was targeted/affected in the attack.