If you’re using Modern activities, you can also utilize Use app/browser activity. Just set the property Close = always, and Open = never (if the window is already open). To target the correct window, you need to specify it with the window selector (or use UiElement variable).
I’m curious why you want to kill the window(s). It doesn’t really matter if Chrome is open, you can still open and attach to other windows, attach to whichever open ones you want, etc.
You can’t, because the Kill Process activity is intended to kill all the processes based on the name of the executable. You know it’s easy to just deal with the popup using a Check App State, right?