Sorry, the plants are not Wandering Jew but Purple Heart...I dont think that really matters however.

It might but it isn't Likely to make any difference. If you keep it growing in a jar of water for a long time, most likely you'll just get algea growing on the roots and jar which also probably won't make a difference to the plant.

If you're just rooting it and then plan to transfer it to soil then it won't be there long enough for sun hitting the roots to ever be a problem other then too much heat but these plants would do best in indirect lighting anyways.