Is there anything that holds the arrow in place when not drawn, or does the arrow just lay on top of the launcher arm or riser?
No, it doesn't need a holder though they still do come with one. I don't use it though. My arreow just sits on the riser (notice the strip of felt on the front of the shelf) and the launcher arm spans the entire width of the "hood" so it will pick up your arrow no matter what angle you are holding your bow.
Can you lock the launcher in the up position like the QAD'sand Ripcord?
No, it still works like the original TT's. It doesn't need to have this fieature the way it is designed.
However, for what it's worth, a ripcord is a close second choice for me.