As to whether it was a mistake to try advantage - it's damned if you do, damned if you don't here.
We've all blown for the foul in this situation just as the attacker lets go a shot that gets past all the attackers into the corner of the net.
(OK I'll bite). Lets assume for the purpose of this argument there was a foul.
Except that this is a different circumstance to the usual damned if you do, dammed if you don't. Its a red card situation and there is 4+ seconds between the foul and shot on goal, 5+ second until the ball goes out.
The offence is a red card offence. You have to decide almost immediately to play advantage or not. Generally it has to be clear opportunity to score a goal (I know the law doesn't specifically include DOGSO but it does included a second cautionable offence which is the same concept).
The sequence from the foul
1. attacker was fouled
2. defender takes two steps
3. defender takes a controlled touch (second attacker not in frame at this point, at least 10 yards away)
4. second attacker takes a controlled touch from 8 yard outside PA to 2 yards inside PA
5. second attacker takes a shot on target with slight angle and only keeper to beat.
6. keeper deflect the ball out.
The first acceptable and on protocol option would have been to blow between points 2 and 3 or immaturely after point 3 here
Ref had enough time to do that. The second attacker would not have taken the first touch let alone the shot on target. Issue the red card and little chance of mistaken identity.
The second acceptable but not recommended option would be if she waited a little, signal advantage immediately after point 4. The attacking team is now in a more beneficial position (controlled shot on target from inside PA with only keeper to beat compered to CFK from outside PA).
You do not bring back to the FK if the attacking team have not converted their advantageous position due to lack of skill more than 4 seconds after the foul. You basically say the same in post 13 (except that its not a goal kick
). Both the touches of the second attacker were wholly controlled.