1/2) To assign you dont 'drag' or 'double-click' there is a button called 'Put on Active Duty'
3) in dont understand what you mean about doff missions being "locked" please try and explain
4) Its a matter of chance,
If you are using white quality doffs, expect failure, even with good traits, green is better but still fairly high fail chance, blue and purple are not guarenteed to work, but most often will be a win
Just to elaborate on it being a matter of chance, i once had 18/100 crew (all blue/purple) in sickbay at a given time, due to terrible luck. Nearly 1/5 of my doff roster in sickbay.. yeah XD
There is a difference between 'need and greed' in the game, like there is a difference between 'need and want' in the forums