I have created a provisioning profile and added an iOS Device to it. When I now run the app with that Bundle ID in Xcode directly on my iOS device, is the provisioning profile already saved inside the app or do I have to archive the app first and deploy the IPA i.e. with iTunes to actually use the provisioning profile and set the expiration date to 1 or 3 years?
Running app in Xcode and Provisioning Profile
Assuming you haven't messed with the signing settings, all you really need to do is press the Run button and Xcode will figure it all out while you are developing the app.
To make a production version of the app, archive it, make sure your current production certificate is installed, and then export the app for enterprise distribution.
Xcode should take care of all the certificates and provisioning profiles for you on the automatic setting.