Can i have limit posts on a specific category and automatically remove older ones?

It seems like you could achieve this by just setting the “Blog pages show at most” setting from the dashboard: Settings -> Reading options.

Alternatively, you could create a custom template for the specific category in question and then set the posts per page equal to however many posts you want to display and order by settings to descending from there. Which would automatically display the most recent most post at the top.