Welcome back, Tyger.

That's quite a few questions. Let's see if I can get them all.

Taking a team into a dungeon yourself (called "command missions") unlocks based on the level of your highest squadron member. I think the unlocks for stuff were at 20 and 40.

As far as training versus missions, it's going to be case by case. For one, you'll want to do training to get your squadron's stats up to the cap for their current level. Afterwards, if you have plenty of active playtime, it's most efficient to do your three training sessions for the day and then the 18-hour mission. It's also worth noting that the training sessions reset daily at, I think, 3 PM EST. So depending on exactly when you play, you may wish to wait for that reset, do three more training missions, and THEN send them on an 18-hour mission.

Oh, and perhaps most importantly, once you do ten command missions, I understand you get a bunch of new emotes for situps and such.