I am trying to find out evidence concerning how to handle both timing and ease of modals/dialogs, popovers, popups, alerts and so on. Is there anyone who can share studies or links?
There is not an exact study which defines this kind of stuff. It all depends on the needs of the design system in place. For example, compare Material Design's modals ( https://material.io/design/motion/understanding-motion.html# ) with the ones from Apple Design System ( https://developer.apple.com/design/human-interface-guidelines/ios/visual-design/animation/ ). You will see that there is not a certain rule they follow.
However, you can find general (extremely general) guidelines, like: https://designmodo.com/design-modal-windows/ , from where you can get some tips of how to make a modal easier for the user to digest.
I hope that this helps you get closer to the answer you are seeking.
You can find some useful information at Material Deign's Dialogs section.