Hi!
The vertical results list cannot have pagination, it only supports a scrollbar solution. The pagination is only available for the isotopic layout.
Pre-defined values are not yet possible, but it is on the list of upcoming features.
Remembering the search values is actually possible. On the Compatibility Options submenu, enable this option: https://i.imgur.com/jEs5ym1.png
It is not perfect, but it should remember most settings/phrases and trigger the search whenever the back button is clicked on the browser.
