1. Before jumping in, it is good to wash first.
2. You are allowed to bring a small towel inside the onsen but do not dip it in the water.
3. Swimming? the water is shallow and hot, how can you swim in it and besides you might bump into the other clientele. I did that but that was when me and my friend where the only one inside that time. Just fooling around a bit.
There are a lot of sites on how to use the onsen, just google
