Re: How to i back up my contacts?
As long as you have your Contacts set to auto-sync in the main Settings menu, it will always backup to your Google account in the cloud.
I assume you're talking about your Note 2, right? I don't know how different that phone's People app is from the one that is on my Nexus 5, but see if you can follow these steps (wording might be different:
1. On the main screen of the People app, tap Menu
2. Select "Contacts to Display," and if possible, choose "SIM" or "Phone account."
3. Tap Menu again, then Import/Export, then Export to Storage.
4. Once that is done, tap Menu again, then Import/Export, then Import from Storage. Make sure to specify to import into your Google account.
I've actually never done this process myself, so one thing I can't be sure of is if you can export your SIM contacts only, or if will export your entire contact list (including the Google contacts). If it exports the entire contact list, and then you import it, it's possible you might end up with duplicates.
There are probably other ways to do this, including using 3rd party apps--I'll let others chime in about that.