Right now, I'm not aware of a way to trap the F3 key and invoke a script as a result.
For the enter key, you can link a text field to a script button so that if the focus is on that field (e.g. you're typing into it) and you press enter the linked script button is pressed. The script button can, of course, be hidden. I don't believe you can trap the enter key in any other context.
Steve.