Don't worry about apps that are automatically opened by the system--that's how Android works. It is counterproductive to close apps routinely to "clean RAM." See these articles for more info:
http://forums.androidcentral.com/ambassador-guides-tips-how-s/380592-guide-ram-android.html
RAM: What it is, how it's used, and why you shouldn't care | Android Central
Antivirus apps are also generally not necessary, unless you tend to be careless with your internet habits, so if you're able to, I'd suggest just uninstalling Norton 360. For the most part, it's still quite difficult to get an actual virus on your phone, because malware requires you to manually accept the installation (which is why they try to fool you into thinking you're installing something legitimate). Use common sense:
1. Avoid shady websites that deal with things like porn, gambling, and "free" (aka pirated) apps/music/movies.
2. Never ever tap on a link that appears in a popup while browsing, especially if they're warning you that your phone is infected--they're just trying to scare you into installing some bogus "antivirus" app that is probably malicious itself.
3. Only install apps from well-established app sources like Google Play Store or Amazon Appstore. Read a bunch of app reviews before installing an app to look for any complaints about adware or suspected malware.
4. Turn on Google's "Verify Apps" function. This allows Google to periodically scan your phone's apps to look for malware. It's usually in your Google Settings app, under Security (although it might also be in the main System Settings, in Settings>Security).
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