It doesn't really matter whether you delete an app or not, thats nothing more then software running on the phone, so whether the app exists on your phone or is deleted from the phone, it really doesn't matter at all.
The IP can never be blocked. This is controlled by your cellphone carrier or your ISP when you use wifi, either of them have an IP and it doesn't matter what you do on your phone. They always know its you no matter what, and that info is always logged.
Some think because they browse the internet with a proxy server that the IP is hidden, but those are people that have no idea what they are talking about. That only hides the IP from a site that you visit. It has to go to your carrier or ISP first before ever getting to a proxy server, so your information is still always connected to you.