Hello,
Yes, it’s possible to set the posts in the Masonry layout, as 4 columns. Simply enter the Posts tab in the page editor, choose the categories of the posts you’d like to display and select the content layout as Masonry.
Regarding the single post page, of course it’s possible to add a Posts widget which will display a list of the posts of your choice. However, it’s not displayed as a dropdown menu, but as a list.