Haggar claims she and Alfor were romantically involved at one point, but in the original series she made a remark about how she was never "young" - and even if this wasn't to be taken literally, its context meant that she was never infatuated with a lover in youth.
The gemstone is roughly the size of half a palm in diameter, but when Allura first puts it to use, it easily fits in half of her hand.