I'm glad to see that you are considering the Qt component. Qt looks good on Gnome, KDE, and other desktops. It is also relatively lightweight for what it offers.
The majority of Linux users use a GTK desktop, IMO WebkitGTK would be preferable.
I use a GTK desktop on my Linux desktop computers (Ubuntu/Debian and Kali). However, I prefer Qt applications. They look very well on my GTK desktop.
No - that's built on webkit, which is apparently becoming the next IE.