I cant confirm if you will have any speed increase but yes you can connect the dlink router to your broadband modem and stop using the apple basestation.
How do you have Mac OS X installed on your HP system, unless you did it with the illegal OSx86? If you did, which you must have, then there is no guarantee that anything will work with it, because it is hacked software and has little security.
Yeah, with the G4 the Airport Extreme is you will need. Along with that you will need a router(base station) to connect to your modem. You don't need to buy Apple products for the router, although they do make things easy. When you have the AirPort c...