[Q] I can't update phone, also general questions about rooted device [New user] topic

Hello,

I just got and Samsung galaxy S3 from a family member. And first thing I did, was reset it to factory settings. Which went ok.

Now I would like to update the phone. Current android version is 4.1.1. When I go into update section of the phone I get message that current phone version is up to date, but I read on the internet that latest version is 4.4.2. How should I best proceed in order to update the phone.

Also, I have several questions which I've been wanting to find out (Please note that I'm quite new to android):
1. This phone was rooted. It appears that after factory reset it is still rooted (According to Titanium Backup) is that how it should be? I thought that after factory reset phone would not have root access. Also what is strange, that after performing a factory reset I already had quite old version of Super Su pre-installed and CyanogenMod file manager, why is that?

2. I have an AT&T version of the phone. But I live in Europe where there is no sign of AT&T. Is it possible to remove AT&T branding? Also this phone has some kind of custom Adnroid software update "AT&T software update", which always tells me that v4.1.1 is the latest version of android available for my phone. Is it possible to revert back to native software update?

3. I did a factory reset on the phone about 30 minutes ago, how it already has 5.5 GB of free space used?

4. I found the application named "System app remover". Can I trust its judgement on which apps are safe to remove?

5. How can I make sure if I have 2core processor or 4 core processor?