First of all, monitoring and logging the http/https request response cycle from your android / iOS is a pretty difficult task. I wonder if Android and iOS even allows it. So, as far as I know, there are no such applications that track all the request-response cycles on your device.
But remember there is always a walk around for everything.
Introducing GlassWire 
GlassWire is an application that allows you to see your current and past network activity. It is available for Android and Windows. Download links below.
It can you the the exact information about all the requests-responses made from and to your computer. Unfortunately, this feature is only available to the Windows application and not on android.
The windows application how ever records and stores all the information about how much data has been consumed in any given time. It also shows the live data usage in beautiful animations, it also gives details on how much data is used for a particular protocol and particular host. This serves our purpose.
Connect your Android or iOS device to a personal hotspot of your Windows PC, and voila, you have it.
Source: My Quora Post
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Additional features of GlassWire
Other features of GlassWire include Network Monitoring, it gives you the details of other devices connected to your network. It also includes a built in firewall that allows you to break an app’s connection to the internet. And also shows which app is or has connected to what IP address and their country of origin.
Well, there’s always a catch. You have buy a premium version of GlassWire to have all these and much more features available to use.
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GlassWire
GlassWire is an application developed for android and windows for network monitoring and firewall.
Operating System: Android, Windows
Application Category: Network Utility,
