Do Apple phones have built in security software?

Unless you jailbreak your iPhone, I don't believe there is any way to install and run a virus on an iPhone, as the only way to run software on it is through the App Store. The App Store does not have malware on it and all the apps will not harm your phone. But be careful what apps you install anyway as some app's privacy policies are not so friendly. I hope this helped!

iPhones have all the security that you need and Apple provides frequent updates as well.

You don't need Norton. It will do nothing useful for your phone.