I've never paid enough attention to notice how quickly mushrooms spread on their own but it is relatively fast. If you want to hasten their proliferation you can cut them up with a razor blade. I dont think its necessary to include part of the mouth with each fragment but it may help. Getting the newly produced fragments to stay put is the hard part. Usually a small plastic basket with rubble on the bottom works. Just toss all of the pieces in there and give them time. After several weeks you should have many small mushrooms attached to rubble that you can re-distribute through your own tank or sell/trade.
Opinions on dosing will vary. I dont dose anything to my soft coral tank, I just feed the fish and do water changes.
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