It is the Vulcan Ambassador mission where an Udine is disguised as a Vulcan Ambassador. I completed the mission and destroyed the Udine ship in orbit. Then I got a phone call and I talked to the phone. When I got back there was a red window message telling me that there is nobody in this system and I can warp out. I warped out but the mission still showed in progress although I had completed it. I warped in the same system and the map was reset. Is this is a bug or a mistake from my part? Namely should I leave the map when I complete the mission without delaying much?

Another problem was related to the Vulcan Sector Patrol - Bhea System. When I got there there were Orions but no shipyards. I destroyed all the Orion ships and left the map but the misson was shown as still in progress. I re-entered the system several times with no luck. Finally the map reset and this time there were both Orions and shipyards. I destroyed them all and this time the mission was listed as completed. Am I doing something wrong? Or is there a general instance synchronization bug in the game?

Finally what is the jump to instance feature?

the first part happened because you went "out of bounds" so to speak, or the edge of the map. which happened of course since you left your pc and your ship kept moving. all you need to do in that instance is turn around and head the opposite direction. if you say yes to the popup window, that will mess you up obviously.

i can't help you on the next two questions.