I think I can answer #1. Please, correct my math if it's wrong since it was a long time since I did this in school.

1a) Assuming a ship drop rate of 0.5% and 24 keys

1-10^(24*LOG(1-0.005)) = 0.1133 i.e. about 11% chance

1b) Assuming a ship drop rate of 1% and 24 keys

1-10^(24*LOG(1-0.01)) = 0.2143 i.e. about 21% chance

In either case the odds are against you.

EDIT: Sorry, I misread your question and my calculations were made for a JEM ship drop with 24 keys, not a BOX ship drop since we have no idea how high that is. But the odds are probably a lot better.

EDIT2: Lol, I'm completely out of touch now since the Jems don't come in the boxes but in the reinforcement packs as you correctly write. Just replace 24 with 7 in my calculations above and it should give you the number. This is what S7 grinding does to my mind