If officer Darth Vader is used on a VSD II attack with Miniter Tua being discarded on the VSD II attacking to reroll dice does the VSD II get to keep the ECM that Minister Tua allowed it to equip?

In this case officer Vader being on a Gozanti at distance 1-5

Yes Tua effects things in the fleet building stage. Once the game begins you can choke Tua for rerolls and the ECM stays on the ship. Captain Needa is very similar keeping the evade.

Titus & officer Ozzel also have their game effects early in the game and make perfect choking targets for rerolls with Vader.