Yes, the word 'beautifully' is an adverb modifying the verb 'developing'; for example:
Your garden is developing beautifully.
Her eloquence fit beautifully in a sentence. The nightingale sang beautifully.
He was acting so beautifully like as if he was an angel.
"Beautifully" is an adjective and can be used to describe something. Examples of such are:"It was all beautifully done." & "She sang her piece beautifully."Placement in the sentence is up to you, of course, as long as it's used as an adjective.
The food was cooked beautifully in the restaurant. This is the sentence using the word cooked.
The woman was beautifully dressed and looked very elegant.
Yes. For example: The ballerina beautifully spun around in a circle.
The organization is developing plans to make more water wells in Africa. Developing a topic sentence is hard work. Using the word 'developing' in a sentence often requires a passive verb.
That is not proper
A singer I know was asked to sing in a band, and she sang beautifully.
To use "sung" in a sentence: "She has sung beautifully in many concerts."
I am just not interested in playing the bassoon.
I went to see the musician play at the concert.