I'm no expert and will probably be corrected here, but IMO, php is a server side language, which means it does its thing before the page is sent to the browser. So in essence, php does its thing and sends the result (usually as html) to the browser (the client). So yes, you can use php to add shortcut keys to a page but not directly - it can output html (and js if required) to do so.
Printing via php is certainly possible, but I don't know whether this will ensure that you print from the server or the client machine. I assume the former, as grabbing control of a client's (user's) printer would be a no-no IMO.