Data toll tripled from Android to IOS, no changes in usage habits. How to troubleshoot? Possibly redirect and sniff (tips on how)?
You have multiple questions here, so one answer at the time:

When your iPhone is connected to a Wi-Fi network, any app that needs data from the Internet will use the Wi-Fi network instead of the cellular data network. The data usage is therefore not counted against your monthly cellular data limit. However, when not connected to a Wi-Fi network, any time an app needs data, it uses the cellular data network and is counted towards your monthly limit.

Stopping apps from using Cellular Internet data:

That can be done in your iPhone settings. Select Cellular and it will open new window showing who and how much. There is a slider to turn that app off from Internet data.

At the bottom of the list, there is an item named System Services. Selecting it will show how much cellular data is being used for things like Messaging Services, Push Notifications, Documents &amp; Sync, iTunes Accounts, Siri, Voicemail, Software Updates, Find My iPhone, Diagnostics and Apple ID Services.

Remember those are cumulative data, so rest them once a month in date accordance to your plan.

There are few external apps for measuring and controlling internet data.

For Safari and FireFox, go to the individual settings and disable the FlashPlayer to prevent sites loading unwonted flash based advertisements. You will be asked to enable it if you do want to watch something.