Summary (of what is probably true):
1, You need to be Shipyard level 2 to get Cache Missions
2, BRF progress affects HFC Cache level (between 11 and 19 kills, you get a Cache that is one level below your BRF progress.)
3, HFC kills give you the Cache of the same difficulty - Heroic kills, Heroic Cache, and etc (see Note 1.)
3, If you fail your mission, it will respawn (see Note 2.)
Thanks to good luck (and 20 Mission Completion Orders, 15 of them stale inside my mailbox), I've successfully upgraded my shipyard to Level 2 and completed the Cache mission a few hours ago, before 24 hours has passed since patch. Since I did not even so much as step inside HFC, I was pleasantly surprised to see a Heroic level Cache. I bought a 10/10 M-BRF run some time ago after giving up progress, giving me a total of 19 Mythic kills inside BRF (1 Blackhand).
Just thought it's about time to pool information on this subject. It would hopefully be useful for other people if we can share our HFC kills, BRF kills at the time of triggering the Cache, Cache level and Cache drops. Maybe Highmaul? I doubt it actually will affect the cache though.
......oh, and the cache contained a 705 Chest piece from Hellfire Assault (Felgrease-Smudged Robes.) I have a warforged 706 chest.
Note 1:
Note 2: