Will the program make the browser pop up/become active when a keystroke is passed to the browser?
Oh, you still want to pass it to the browser? AutoHotKey I[/I] can send a key silently to the browser. Not sure how it would be received though, never tested it.
Can the script be run on the users computer without him having to do anything?
The user would need to download it, if that's what you're asking. I'm pretty sure you can't do it any other way, though, meaning without them downloading something.
Can I make the program target my site only or will it affect the browser even if the user switches to another website?
Hmm... not sure. You'd have to test a little. I could test a little, too, just to make sure I'm giving you a plausible idea, lol.
I know AHK can silently send keys to another window, but sending it to a specific tab, I don't think so. I don't know of a way to switch tabs with AHK because I'm not sure if AHK has image recognition or not. Would need testing.