[Q] New to android - problem with Note 2 Android update topic

Hi
I am new to Android. I have been using blackberry for many years. I got my Samsung Galaxy Note 2 LTE a couple of months ago.
I was just using the google play store app to download and update apps, nothing complicated

Yesterday i received a message to update my android os to version 4.3
My carrier is MTN Cyprus

So i followed the steps and it worked
But for some reason, when my phone boots, i see the logo of a different carrier! I see VODACOM instead of MTN Cyprus!
There are also vodacom applications that are useless and i cannot remove them

I have been talking with my carrier support since yesterday and searching forums and the web for a solution
So, i have a few questions:

1. My phone looks OK, everything is functional as far as i know. Will it be a problem if i just keep it like this?
2. Can i remove the unwanted stuff somehow, keeping the new android os?
3. I am reading about custom ROMS and rooting. Can i install a fresh android rom myself, replacing the current one, without waiting for my carrier to release a new update? Do i need "root access" to do that?
4. Can i install any android 4.3 on my device, or it has to be a specific version for my device?
5. If i root my device, are there any risks? is it legal?

Thanks