[Miss Lockheart]

Mostly!

Though actually the chest in the Phon Coast is the fourth one not to touch (I would leave all sixteen just in case), the Zodiac Spear is in a chest in the Necrohol of Nabudis, I think.

Barheim Key-

Content Hidden!

complete the Dalmascan Patient and Missing Cactoid sidequests. Once you've finished them exit the village, come back and talk to Dantro's Wife again, who will tell you that the patient is behind her house waiting to say thankyou. Depending on how many items you gave her during the quest you will meet either a Bangaa, a Hume or a Moogle. All three will give you the Barheim Key, but you will get another item depending on who you get. If you get the Moogle, the best possible outcome, you can get a Golden Amulet early in the game.