If two PS 3 hips fire at each other, the one without initiative has FBA. The player with initiative shoots the FBA shirt down, but he still gets to attack as he is the same PS. Can the second ship use FBA? It is not an attack, but takes place in lieu of one. Secondly, he really cannot take any more damage.

Is there an official ruling on this because I cannot find one.

From the relevant rule section:

If a ship would be destroyed and it has the same pilot skill value as the active ship but has not had an opportunity to attack yet, it is not destroyed. Instead, it retains its Damage cards and continues to function as normal, suffering any effects on its Damage cards.

So, you can use FBA as it's used during an opportunity to attack. And just because the ship has enough damage to destroy it, doesn't mean it can't take more damage. It's also in the FAQ that a ship can use FBA before being removed under the Simultaneous Fire rule.

If a ship equipped with Feedback Array destroys an enemy ship of equal pilot skill that has not attacked yet, that ship may still perform an attack (or use Feedback Array) before it is removed

Italso applies in that a ship that has simultaneous fire and more damage than its hull can still tske more damage from another ship of the same PS. Might be worth it to push more crits through.

Exactly. If you can give it a crit that stops it from firing back, you're safe. So it's worth a go.

Never thought of pouring more damage in hoping for good crits... Hmm...

Hit him til he's dead, then hit him some more!