system upgrade, firmware, USB debugging problem

Hello everybody,

I bought a Samsung Galaxy Note 3 (SM-N9005) phone. Firmware: N9005ZHUENF1. Android 4.4.2.

I tried to update the system, but the phone said "I am fresh". But, it is not true, because my girlfriend has a same phone and it updated across the OTA.

I installed the KIES to the my PC and my phone do not work with it. When I connect the phone to the PC with a USB cable, not working. When I connect my girlfriends phone everything nice.

I enabled the USB debugging mode, but it is not working. When I connect the phone to the PC with a USB cable the question is not arrive that I would like to enable the debugging mode. When I connect my girlfriends phone everything nice.

I think my phone is rooted, because I checked it with an app, and the app said "Yes, rooted".

My questions are:
- is it possible to upgrade my phone to the Lollipop?
- is it possible to put into the phone the original firmware (if it will be necessary)?
- is it possible to enable the USB-debugging mode?

I am waiting for your asks.

Best regards,

Zoltan

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