First of all, you should ask your girlfriend if she really needs to back things up using Verizon's system. VZW's Backup Assistant, in my opinion, is clunky and completely unnecessary if you have a Google account, because Google can constantly back up all of your contacts and email and calendar appointments and photos on its own. Backup Assistant probably also bogs the system down, especially if it's running in the background. I've never started Backup Assistant, so it's not active on my phone--unfortunately, it isn't possible to disable it, but at least it isn't active.
Regarding Verizon's antivirus app--it's probably fine (I think it uses McAfee's software), but it's also probably not as good as others out there. And running 2 antivirus programs can cause conflicts. If the Verizon antivirus app was preinstalled, then the only thing you could possibly do is to disable it (by going to Settings/Apps/All, selecting the Verizon antivirus app, and tapping Disable if the option is available). If it's uninstallable, you should see that option there as well. In my opinion, your friend should disable or uninstall the Verizon app, and stick with Avast, which has a good reputation.