Seachem Flourish is a fertilizer. Seachem Flourish Excel is a CO2 booster. It took me a while to figure that out too :)
How big is your tank? What substrate do you have?
As far as I know, anubias and Java fern need nothing to grow. My friend has a betta in an unfiltered/heated bowl and her Java fern and Anubias look great. You don't need ferts for those two plants, but it wouldn't hurt them.
I don't know much about the other plants, so someone else can tell you more about whether or not you need to use ferts, but as far as ferts go, there are a lot of methods. If you have plants that don't use roots to get nutrients, but take them out of the water (like duckweed and hornwort), you can use a liquid fert. For plants that use their roots more (like amazon swords), you can use solid things like root tabs, or put a layer of top soil under your sand or gravel that the plants can get nutrients from.
As for your duckweed, personally I would be worried about it outside. I am a worry wort, so I would be scared some animal would fall in the bucket and die or something. I know that duckweed grows like crazy and is almost impossible to kill, so be prepared for major population control of it. If you get enough, just put a bit in the pond and a bit in the tank, and watch it take over. You probably could also just put all of it in the tank, and once it takes over, take a handful or two and stick it in the pond.