In regards to the plant cutting. Cut to the base as far down without touching the roots or new growth. I know about java fern, it's a great beginners plant. Old leaves adjusting to your tank might have black spots grow on them. It's kind of a slow grower and is a rhizome plant. This means the the thicker green base where leaves come out shouldn't be buried. The black roots that come out of it can. People also like to attach the plant to things like rocks or wood. The java fern has also low light requirements. I have no experience with frogbit.