If radio.begin() is like calls (SPI.begin() for example), it needs to be called before other radio.(commands).
Look at the markings on the chip - you should be able to clearly read it and compare it to the nrf24L01+ datasheet to see what you have. If not, use a more reputable source on your next purchase.
The numbers you presented in Reply #2 have a '+' in them which I suspect is significant.
From a quick read of the nRF24L01+ datasheet it does not seem to have a register that returns data to identify its type
I suggest you read the datasheet under the heading "Ordering Information" where it specifies how the devices are marked. You may also need to look at the datasheet for the older device.