Apple uses app signing to control what can be placed onto a phone. Sideloading apps (installing an app not through the app store) require a valid developer signature, provided by Apple, to install. Or, applications can be installed by jumping through hoops to trust an unidentified developer. An iPhone won't need anti-malware in this regard.
The best way to ensure an iPhone doesn't wind up compromised, is to never trust unknown apps, and to only get apps from the app store. Despite what others warn/say, keep your apps up to date and also keep your OS up to date. If you sync your phone with a computer, keep that computer secure, in the event a piece of malware targets iTunes/iPhones someday.
Apple will remove apps from a phone that are found to be malicious automatically in the background. This is very rare to have happen because of the way iPhone app approval takes place. It does NOT apply to applications not installed through the app store - those will eventually wind up blocked from running.
As for identity theft apps... look at one of the numerous services out there advertised on TV/Radio. For finding your iPhone's privacy settings, check Settings > Privacy and also check the settings in each individual app. iPhone apps are sandboxed and will not be able to leak data across to other apps unless you explicitly grant the app permission after the fact. You can clear your browser history / cookies / saved passwords / etc in Settings > Safari.
We're always here for support. May we ask if you have been able to contact Apple regarding this concern? As our devices are created by our manufacturer's we always recommend to contact them as they are the provider.
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