Hi
A real nRF24L01+ should look like this.
Unfortunately it is not very difficult to duplicate the marking of the chip, and a fake chip can't always be detected by the marking alone.
Still, if you let me know the marking on your chip I can tell you if it's an obvious fake.
I think the best way to find out if your problems are caused by a fake chip is to buy an nRF24L01+ module from a safe vendor (such as this one from Sparkfun) and check if it exhibits the same issues. If it doesn't then you probably have a fake on your hands ;)
Best regards
Torbjørn

The marking is similar, but the last line is different - the big distance from the point to the letter N.
Read all the registers from 0x00 to 0xFF, all the same manufacturer. Register 0x1E on all chips reads 0x68?
Hi
I did a register readout on my own genuine module and attached the results below. Getting 0x68 on register 0x1E appears to be normal:

I also found an interesting forum thread discussing fake nRF24L01+ modules. There might be some good information there regarding the different fakes out there, and what differences you might see in performance and functionality.
Best regards
Torbjørn
I have all registers with factory settings, and you have 0 and 5 differ!