I answered questions in your log, but I'll try to answer here what wasn't covered there.
Java moss doesn't have a rhizome (java fern does). It just takes some time to attach to things, so thats why its recommended to tie it down. If it is staying on the wood, I would leave it.
The plants should be fine without any supplements. You have low light and low light plants, so usually they grow fine (but slow, which is expected) without supplements. Something you may want to look into in the future is a combination type fertilizer called Flourish. There are several Flourish products, but the regular one (just called Flourish) is a mix of micro nutrients. Here is a link to a pic and information:
http://www.seachem.com/products/prod.../Flourish.html.
With more light comes the need for more nutrients.
Right now, you should be fine though.