While defending while Hidden can Davith discard Hidden using Covert Operative for +1 block and during the same defense use Force Illusion to become Hidden again and then trigger Elusive Agent to recover 1 strain?

Force Illusion seems to imply it will be used to help friendly figures but appears like it's valid to use on an attack targeting Davith (assuming he has LOS to the attacker).

Yes you can do it, but use Force Illusion at step 3, so that you become hidden before applying modifiers.

9 minutes ago, Trevize84 said:

Yes you can do it, but use Force Illusion at step 3, so that you become hidden before applying modifiers.

Covert Operative triggers on step 4. If Davith starts hidden (see OP), if you play Force Illusion before, trying to make a hidden figure hidden does nothing. In that case you should thus play Force Illusion just after resolving Covert Operative.

Naturally needs reciprocal line of sight. It's possible for the hostile figure to have line of sight to Davith without Davith having line of sight to that hostile figure.

1 hour ago, a1bert said:

Covert Operative triggers on step 4. If Davith starts hidden (see OP), if you play Force Illusion before, trying to make a hidden figure hidden does nothing. In that case you should thus play Force Illusion just after resolving Covert Operative.

Does it trigger at step 4 because it's a while-defending effect that modifies dice results? If so, should I consider "effect that modifies dice results", any effect that adds/removes accuracy/damage/surge/block/evade/dodge?

Any ability that is resolved "while attacking" or "while defending" can be used at any point during the attack with the following exceptions:
...
-- An ability that allows a player to modify die results can only be used during step 4 of the attack. (add or remove symbols or accuracy)

and

4. Apply Modifiers: If players have any effects that gain or remove icons or Accuracy, they are applied at this time.