How to setup login functionality, for people who want to save posts on my site? I need to make register/login screen and after that people will see the same home page, but with saving icon after post title and icon in top right corner with number of saved posts?
I hope you are well today and thank you for your question.
To achieve this, you have to develop custom code in the child theme of Gillion theme.
Developing custom code for custom functionality is beyond the scope of support that we provide here. Please see https://themeforest.net/item/gillion-multiconcept-blogmagazine-theme/19470306/support
If you are not a developer then you can consider hiring a developer to develop it for you. You can hire a developer from any freelance site. Shufflehound recommends the developer https://www.upwork.com/freelancers/~011652ffec8865c6d5
You can display login / register links in the site menu using below plugin.