Re: How long does it take to get my business account approved?
A business account in general does not need to be approved. You can get up and running with that pretty much instantly, and you can pull live API credentials.
For REST Apps you would need to create the app under your developer account at https://developer.paypal.com, and then make sure each of the features you need are enabled for it and submit accordingly. Depending on the features this could be approved immediately or may require further vetting, which could take a few days.
Angell EYE - www.angelleye.com PayPal Partner and Certified Developer - Kudos are Greatly Appreciated!