Because it has to run as an online dogfight, is there a way to disable respawning, to make it seem more like a normal Single Mission?
No. And I don't get the purpose for such thing to do. If you want to fly in same Flight with different plane than Flight has, there is no way.
If I get it right, what you may want is this : Place a generic stationary plane in Home Base for you to spawn at this position. Make a flight
(or flights) to taxi for take off & then join them with whatever plane you want. But in Dogfight (MDS), player cannot be assigned in any AI
Flight. Only in single or cooperative missions.
Moreover, can online dogfight missions be set so that "MISSION COMPLETE" or "MISSION FAILED" also appears?
Yes. If you place Target objects as in Single missions, you get "Primary target complete" etc & if you accomplish all primary targets
in timer's duration (if set for accomplishing targets), you get "Red Won" or "Blue Won".
What is great about MDS missions is, that you can have AI planes, ships or vehicles spawn at different times during the ongoing mission, fighting each other &
flying for different type of sorties (eg. Bombing, escort, cap, air superiority, dropping parachuters etc), which can last for hours (until one
of the 2 sides accomplishes their targets), while player (or players online) RESPAWN/REFLY after each sortie they make, to assist the AI's for mission
accomplishment of their side. This gives the feel of an ongoing battle, dynamically affected of player's actions. This is what MDS missions it's about.
Though UP3 is the best at this type of missions, in DBW, SAS Modact or HSFX, you may have the same result, though with less capabilities
(like rearm/refuel & moving frontlines with capture of AirBases that don't exist outside UP3).