When my phone rings, the screen is automatically turned on. Home button will also turn on the screen and can be set to answer the phone.

 

Are you using the stock home screen? I use Launcherpro for my home screen but when I do I cannot use the double tap to close my screen, it will open the screen though. If you aren't using a stock home screen then change back to it and see if you then get full use of the double tap function. If you are using the stock screen then try switching it with the biz version, restart the phone and see if it works.