Can the same app work on Android and iOS?
Many of them carry the same title as the app store version, but can be quite different. A Droid cannot directly access an iPhone app, because they use different formats. IPhone apps use ipa, while the Androids are apk. Therefore, developers have to code one version of an app for Android, and another for the iPhone.
Can I use 3rd party apps on iPhone?
Your iPhone will automatically trust any app downloaded via the App Store, as they have been evaluated and verified as safe by Apple. Third party apps offered for download from other sources will require you to go through a multistep process before your iPhone will "trust" the apps and allow you to use them.