The phrase “duly noted” is very common, but I have never used the word “duly” outside of this context.
What is the meaning of the word “duly”, and what does it add to the word “noted”?
I would also like to know if there are other uses of “duly”, and if it can be used on its own.
Duly is the adverbial form of the adjective due. It means either properly or punctually, and can be replaced by either word felicitously. So duly noted means correctly or appropriately recorded.
Duly noted encompasses only a tiny fraction of the usages of the word: this Ngram should be sufficient to illustrate:
Duly is as independent as it could wish.