In the following sentence, can I use the zero article before 'important means' instead of 'an'?
Newspapers are still (an) important means of communication.
Yes, you can omit 'an' in the sentence 'Newspapers are still (an) important means of communication.' When the 'an' is omitted, the word 'means' becomes plural. It happens that the singular and plural forms of 'means' are identical.
zero article == no article
.