1. The ambiguity is best described in lines "I woke and chid my honest fingers, -- / The gem was gone". As if her fingers could have kept the jewel with her sleeping. Even though she did everything she could to keep it (her fingers are "honest", that means innocent), she still lost it somehow. Maybe it was meant to be that way.
2. The jewel is figurative - it means it's not an actual jewel, but rather a metaphor of love or beloved whom she had lost. The fact that she talks about a gem gives away many associations: this love was something precious and exquisite for her.
3. It doesn't matter where the gem "went", and the speaker doesn't give us any clues about it. It's as if she doesn't even think about it. The only thing that matters is that it's lost to her, and will never again be in her possession. It's a one-direction journey.
4. She went to sleep because she felt calm and secure about her gem. It was a nice, idyllic love, something that made her serene and happy, so she started taking it for granted, and didn't realize that it could go away anytime. The warm day and prosy winds convey this feeling. She was lulled by it.
5. Considering that all things, good or bad, must pass, memory is indeed all any of us own. Memory of good and bad things makes us who we are. However important something might be to us, one day it will surely go away, no matter how hard we try to preserve it and keep it safe.
