url routing, friendly url

It depends what you want to do in your application and what seofriedly you want.

Slug can be like 'animals-african-elephant' and this way you can use $segment = $this->uri->segment(1) but if you want urls like this 'animals/african/elephant' you should use uri_string() function from Url Helper library.
Also you can use get method to send params with slug like 'animals/african/elephant?page=1&sort=name' and then get data like $this->input->get('page');

You should check if array index exist in this line: $id = $get_link[0]['link_id'];