Yes it is possible. You can goto list view of your contacts. Then select the contacts you want to merge together. And click the action button. There you can find an option to merge selected contacts together. Only one of it stays.

Yes, you have to install a app called data cleaning and then you have to set a rule for search especific information. 

I will link you a yt video: https://www.youtube.com/watch?v=ljdLnFAnnmI

Dear, we are facing a situation where for some of our user this option does not show. Do we need to give some permission for this?

This app makes a serach for duplicates each time you save a partner:

https://apps.odoo.com/apps/modules/11.0/partner_duplicates/

Hello 

use below module for search/remove duplicate data.

https://apps.odoo.com/apps/modules/13.0/eq_merge_duplicate_data_extended/

Is there a way to do it automatically ?