a) Qt doesn't use native controls on any platforms (though for half of desktop Linuxes Qt is the native toolkit). Qt has its own controls that are styled to look like native.
b) The screenshot shows Qt widgets. This is not the intended way to do Qt on mobile platforms, and thus no native styling is provided. QML is the official way to do mobile apps with Qt.
Point A is interesting because you can see particularly on OSX that it is not native, despite widespread recommendations to use Qt for cross platform development. I have used wxWidgets on multiple platforms and despite its idiosyncrasies, I have found it performed very well and is obviously truly native on all platforms (unless you choose wxUniversal as a rendered; nobody does) or unless you do "owner drawn" stuff and paint yourself. In any case I would not hesitate recommending wxWidgets for native controls over Qt.
Other minor Qt annoyances include their own scrollbars which ignore the system setting of "jump to where I click the thumb" setting etc.
a) Qt doesn't use native controls on any platforms (though for half of desktop Linuxes Qt is the native toolkit). Qt has its own controls that are styled to look like native.
b) The screenshot shows Qt widgets. This is not the intended way to do Qt on mobile platforms, and thus no native styling is provided. QML is the official way to do mobile apps with Qt.