Direnk

You can clean up your css code as a first step. Especially if more than 1 coder worked on the css files, there could be duplicates and inconsistencies. There are many useful tools for that on the internet. You can try proCSSor for the beginning.

I think you should try Total Cache plugin and MaxCDN.

I am using Monroe theme,

https://themeforest.net/item/monroe-responsive-wordpress-magazine-news/full_screen_preview/3144261

Pagination of single category sections works well, as you can see in the demo, but homepage is not working. Do you need any other code?