Welcome to Android Central! Which tablet? I've never heard of a system app called "google.system.s." Are you saying that something is telling you to install that, and also told you to install 360 Security? It sounds like the tablet might have adware or possibly malware. I've seen posts about 360 Security associated with various suspicious behavior.
I'd consider a factory reset, but first, go to Settings>Backup & Reset and uncheck Automatically Restore. Then do the factory reset, and then after you're done with the Setup Wizard, go immediately to the Play Store and stop any app from installing automatically. Now see if the problem persists.