How can I have a view to load more rows on clicking a "Load more" button?
Looks like Views Infinite Scroll  is a good option for you:


  Views infinite scroll allows you to load and display pages of any view inline, using AJAX (this has been called infinite scrolling, load more, autopaging, endless pages and more). The pager can be triggered with the press of a button or automatically as the user scrolls to the bottom of the view's content.


Here's the pager settings: