Note that simply adding them as included files is not enough if you want the players to edit them, since as far as I know included files are overwritten with the original ones every time the game is run (at least on desktop platforms, unless something has been changed recently in that regard). Ideally you should copy them to the writable sandbox directory and point the player to that location.
No, you can freely edit images from Included Files when exported with the exe and the game will load the new edited images without any issue.
Unless you mean when "running" from the IDE rather then when exporting as a final exe?
I just tested this and the png file from Included Files was exported along with the exe and data.win.
I then edited that png, saved it, and re-ran the exe and the edited sprite loaded and worked fine.
This is a simple use case just to show the functionality of course, and in real world use you'd want to run checks on the edited image to make sure it was within acceptable width/height, reset any sprite origins and/or masks etc based on the requirements of your game.
I'm talking about Windows here too, not sure when on mobile as I have not tested it so it may well work differently there.