OK, like I said it's been a while. If there are no Borg hexes on the map, then you won't fight Borg, because they are one of the empire races, and thus you have to see them on the map to attack them.
To get other ships to help you, they have to request to join your fleet. This was fairly easy in the release version of the game, but I think they made it so that only ships of the same or smaller (or maybe just smaller) size can join your fleet. So, just keep going into hexes that have the ships you would like in your fleet and see if they will ask to join. Sometimes you can just move out and in a bunch of times and eventually it will give you a request. Don't join an AI fleet though, you'll just sit there forever, only let others join your fleet. Once they are in your fleet (maximum of 2 allied ships, if I remember) then they should show up in mission.
Yes, you can alter how much the DV goes down with a mission, and you can also adjust how much DV each hex has. There should be an SFC3 map editor, and you can use that, not sure if it works outside of Win2k (the other SFC2 one had serious trouble with Win98 and Me).