As these two cards appear to share the same timing window ("After you execute a maneuver"), am I able to choose the order in which they resolve? Could I, for instance, move, issue the squadron command, double-tap with Yavaris, and then use FCT to move the squadrons away from the rapidly expanding cloud of dust that used to be an enemy ship?

As these two cards appear to share the same timing window ("After you execute a maneuver"), am I able to choose the order in which they resolve? Could I, for instance, move, issue the squadron command, double-tap with Yavaris, and then use FCT to move the squadrons away from the rapidly expanding cloud of dust that used to be an enemy ship?

Yup, whatever order you choose.

Just complete the full action before starting the next.

Yep, just as Ginkapo said. This is true of all effects in Armada that share the same timing window/trigger. You get to choose the order they resolve in. If both players share the same window/trigger, then the first player's effects resolve first in whatever order s/he likes and then the second player's effects resolve in whatever order s/he likes.