The slowest to respond ship in a tg determines movement delay. Firing delay is on a per ship basis though.
Docked parasites don't matter.
If you are bringing tankers etc. with your battlefleet, consider creating a militarized tanker. It doesnt have to be military, but armor, CIWS, speed, and training is nice in a pinch. Personally, i usually prefer to extend ship range a little and/or create forward fuel dumps.