A:AnswerThe Pioneer NEX is a double-din sized receiver. If your corolla has a double-din sized head unit then it will fit as long as you buy the correct adapter kit. The adapter kit is essential for maintaining a clean look while providing mounting hardware to install the unit. Search for an adapter kit for you corrola to find out if the Pioneer NEX will mate to it.
A:AnswerThe back up camera is an optional ADD ON that has to be purchased and installed at the same time. You do not have to do anything to have it work once it is installed.