I appreciate the intentionality with your 1x01 choices. In accepting/rejecting changes, it often comes down to making sure that the wording has been chosen for a specific purpose.

For the 1x02 crawl, I’d say that the wording is solid, but I would suggest breaking the sentences differently. It’s mostly subjective, but I think it would read slightly better as follows:

Conflicts erupt in the early days of the Clone Wars.
The Republic faces a dire emergency. The leader of Dooku’s army, the droid general GRIEVOUS, strikes swiftly from the shadows.
With a new weapon, the battleship MALEVOLENCE, he has been medical stations, killing thousands of wounded clones.

Obi-Wan Kenobi urgently coordinates the evacuation of medical stations in the Naboo sector, where six have recently been destroyed.
While Anakin Skywalker and Ahsoka Tano lead the search for Grievous, Jedi Master PLO KOON picks up the battleship’s signal and moves to intercept.
But no fleet that has faced the Malevolence has yet survived…

I also got rid of “his new padawan” in order to make room for “and moves to intercept,” which I think paints the situation a bit more clearly.