I think its not realistic to think you can use PySide/PyQt and Python in order to make one application suitable for all those platforms.
First of all the platform you want to develop for should support your programming language (Python) as well as the graphical framework (Qt) in order to make it work. This is mostly achieved by third party developers. If Python runs on your mobile operating system this does not say you can start developing and vice versa.
Mobile development is often done with QML (Qt Modeling Language). This allows you to make really cool and fancy interfaces on many platforms. You can connect it to your own Python code to make a real working application.
At this moment Qt is working on support for mobile devices. Most mobile operating systems like iOS and Windows Phone are not supported yet for the combination Python/Qt and mostly the support for working projects is not really big in comparison to the preferred languages of the operating systems.
Here is a list of mobile OS's which support the combination Python/Qt
Link to projects if there is a good link for a starting points is available
Android: PySide for Android
or if you like to use "webviews" instead of PySide: SL4A
Blackberry 10: BB-py
Meego: Python/Harmattan Project
SailFish OS: Harmattan apps (Meego) run without any problem
For your other questions I have a shorter answer.
The webkit component is intended as a content viewer component. Its not a component for building full HTML 5 apps.
The question which bindings for Qt are better is often asked. What you need to be aware of is that the old version of PyQt did almost the same as PySide. The difference was mainly in the license! However PyQt supports now Qt 5 while PySide doesn't, so make your own choice. I think you can make beautiful apps with both of them.