When creating custom lists of posts pagination won’t happen automatically, you’ll need to pass the pagination arguments into your get_posts call. The full details can be found on the WP_Query codex page.
For the query you want to be paged you’ll need to add something like 'paged' => (get_query_var('paged')) ? get_query_var('paged') : 1; to your $args. And if I am reading correctly I don’t see that you are actually calling the pagination display function in your template, you should be able to add <?php pagination(); ?> where you have <!-- AREA WHERE I WANT PUT PAGINATE --> [sic].
There may be some documentation on using this on the theme developers website, I would suggest reading more about it there, potentially there is even an example you can copy.