As you know, a lot of request (images, scripts, AJAX, etc.) are send when loading a single page. So I need to get all those request and inspect them.
So the question
Look here: https://gist.github.com/kibotu/32313b957cd01258cf67 where you get the http headers at android >=21
The best you can get in your app is the WebViewClient.shouldInterceptRequest
method, but that only has the URL. You currently can't get any of the things you've listed.
For debugging you can use Chrome DevTools if you're using Android 4.4.
The easiest way is to use a proxy. I use Charles, but I'm sure there are others. On the device, go to the WiFi settings, long click the one you're connected to, select "modify network" and enable the advanced options. There you'll be abel to configure the proxy settings for the whole device.