I got my Azolla locally and more recently Duckweed from Ebay. I have not figured out the best way to grow it yet. However growing it in the same place where it is eaten is not a good idea.
I have had the Azolla growing in several places. The best so far is an old 400 gallon spa with partial shade. This Azolla is a healthy looking green and mounds up due to its extensive growth. Currently water hyacinth is crowding it out. In a 35 gallon preform the Azolla is now looking very healthy whereas a month ago it was crowded out by string algae.
I have only had the Duckweed for a couple of months. I split the small quantity (about an ounce) into four locations. The one that is doing the best is inside near a window in a 1 gallon glass jar with a glass lid. This Duckweed has populated the entire surface. Outside in a similar glass jar the Duckweed is not doing as well. Also outside in an open container I have some growing which is doing about as well as the other outside stuff.
If I had to guess, neither Azolla nor Duckweed needs full sun. But there is probably an optimum temperature.