She can only see the summoner spells if she had vision of them previously.... If the jg wasn't warded and summoner spells were used she wouldn't be able to tell unless she gains vision of them. It is only after that the spells become visible on the minimap to her. She can't suddenly see u in fog of war. (have u played as her yet? or watched videos of her being played?)
Her E in no way rewards her for missing it (other than allowing her one tick of her passive). The E may continue to persist as a trap, but it doesn't reward her for missing it. An enemy needs to trigger it in order for her to gain a meaningful "reward". It's a means of zone control.
W, it is agreeable that the shards are quite RNG (both when they appear as well as what spells she'll get)