You can do the same in your browser by opening the developer tools and in fact it comes built in to the browser whereas on a desktop you'd have to install another app like Wireshark/Fiddler to see those requests.
Nothing will. The vulnerability of what happens to your data after it is sent to a third party is the same for any app, web or native.
The biggest difference is that it's way easier to see where you're data is being sent in a browser, since it has built in tools. It's very hard to monitor native app traffic that is sent over SSL.