EDIT: Right, woops - Sorry; didn't see your whole question thanks to a very small screen... Now that I'm on a PC, here goes:
Firstly, to be eligible for mission drops, you would have to have bought the Operation Breakout pass (which is avaliable in-game or from the market).
Now, to get the mission drops, you just have to play games. They don't count to your total drop limit, but you get 2-3 missions every week.
When you get a mission, you'll have to do a specific killing task (or winning competitive maps). When you have completed the mission, you'll get the drop at the end of the game in which you completed it in.
(Note: Mission progress will only be recorded if you finish the game, and not leave half-way)
Answering your question:
To get the gun drops from the three collections, you must complete missions... And, to get missions... Well, they drop just like crates and guns.
You CANNOT get them through regular drops . Only as mission rewards, which can be recieved through regular drops.
Also, as for you not recieving any drops - Could it be that you have already hit the "2 missions + 2 crates + 2 guns" (or something along those lines) drop limit for this week? Or not stay until the end of matches (series of rounds)?