The new Dynamic Duo from the Batman set has a special defense:
When the Dynamic Duo is targeted by an attack, increase the dynamic duo's defense by the attacker's printed damage value.
does this follow the rule of 3?

On team bases, when a figure takes a solo adventure and then the team base is knocked out how many points does that player score. If the team base is at 500pts, does he get the 500pts? Also if he knocked out the solo figure would he get 500pts plus the value of the solo figure?

Increased is a modifier, so yes the rule of 3 applies. If it had said replaced, then it would bypass the rule of the 3.

The player scores whatever the team base was played at, so a 500 point team base would be 500 points. He would also get the point value of the figure that popped off on top of that.

so with a 500pt build if you sent a 177pt figure on a solo adventure, you could score 677pts?

yep yep yep

You could score more if you use some of those new hired assassins, capture some figures, have any vendettas, etc. why limit yourself to only 677 points?

Also, if the Shi'Ar base is being played at 500 points, they can pop off more than just Warstar. You could really rack up the points.