No, there is no built-in firewall for outgoing connections on iOS, and I don't know of a way to install one without using an external device like a router with

No, there is no built-in firewall for outgoing connections on iOS, and I don't know of a way to install one without using an external device like a router with a filtering proxy. The OS limits an app's access to data that belongs to that app, so an app can't gather information you do not give it access too. (e.g. you have to give explicit permission for it to access photos or GPS location). But you do not have any control over other analytics the app may gather and upload, e.g. frequency of app use or info you enter.