I have some more questions for you.

Does a reduced adverb clause play a role of a phrase? If not - why?

What is the difference between an absolute phrase and absolute clause?

Thank you.
I have some more questions for you.

Does a Reduced Adverb Clause play a role of a phrase? If not - why?

What is the difference between an Absolute phrase and Absolute Clause?

Thank you.

He listened to the song, which she played beautifully.
'which she played beautifully' is an adverb clause.This can be changed into a phrase in this way: she played (the song) beautifully. The words in the bracket need not necessarily be present.

Here is a website, but there are many more. All you have to do to find them is put 'adverb clause' into a search engine of your choice.
www.examples-help.org.uk/parts-of-speech/adverb-clauses.htm