About grammar

First things first: "She is so angry and demonstrates indifference to her husband."

"She" is the subject both of the verb to be ("She is") and the verb to demonstrate.

The example sentence does not scan as something a native speaker would write. Your second sentence, which is a question and properly ought to end with a question mark, is not coherent English. You might write: "I would like to know whether or not the verb demonstrate can be used without a subject." Of course, the answer is that "She" is the subject of both verbs.

Thank you for answering my question. It'most kind of you.
I will try my best to learn English well.
Sincere wishes!

I wish you good luck in your endeavor to learn the English language.