No I didnt replace the water at all, just topped it off when the level got a little low.
I used a plain old canning jar, no sterilization no cover just a jar, water, and a chopped up leaf.
The black stem pieces that didnt sprout I just tossed out.
I used artificial lights while the cuttings were in the jar but as soon as I planted them into the media I put them outside in a partially sunny area to harden them off. Eventually they will be moved into full sun along with the rest of my plants.