How active is my mobile phone when I'm not using it? I wonder whether there is any study/website/research work or a place to check how much data my phone is sending when I'm not using it. My question is: when my phone is off, but I'm not actively using it (just left it on my desk) do any of the apps on my phone send any network data to servers, etc.? Can I somehow check this information on my phone (I have iPhone 7) or maybe someone already did such an analysis?
Since iOS 10, I’ve seen very good ability to control activity. Even better, you can see exactly what runs, hour per hour what’s front most and what background apps are taking energy.

If you want no background - just turn that off for all apps. Then review the activity graphs for a couple days. If you want more activity, enable background and remove apps that are more active than you care or selectively disable background activity so you know apps only run when you ask them to run.

If you’re technically minded, the Charles proxy is excellent to log outbound traffic without needing to manage your router. I also use Ubiquiti network routers so know and log access / block some traffic, but that’s on the network side, not the iOS side.
I don’t think getting outside analyses are as important as choosing your apps so you know how they are funding development. If the app is slick and free, you’re paying them in data / marketing / eyeballs in many cases.