For the first part- Samsung has notes on the system updates on their site. I'm not sure what provider you're using, but you should be able to get to what you're looking for if you start at: http://www.samsung.com/us/support/
Use the "Start by Entering..." search bar in the middle of the screen to pull up your specific Note II phone and scroll down to the "Support Overview" section.
For the model I looked up, the "Which version of the Android™ platform does my Samsung Note II use?" question is already in the Frequently Asked Questions list, but if not, use the search bar just about that.
I didn't check every device, but it certainly looks like it's the Kit Kat update that's been downloaded.
For the second part- I'm working off the assumption that your Note is NOT rooted. Upfront note (haha): I don't have a Note II here with me, so I'm going off reference materials and memory on the exact option names in the menus. These steps should let you disable the notification until you re-enable automatic updates.
- Go to 'Settings'
- Click 'More'
- Click 'About device'
- Click 'Software update'
- Uncheck the 'Auto update – Check for updates automatically' option
When the update prompt is in your notifications, pull down the notification list and do the following:
- Press and hold down on the update until you get a 'App Info' option
- Click 'App Info'
- Click 'Clear cache'
- Click 'Clear data'