This is really cool as Qt just looks daunting to start with! Is there a way to make it use native widgets? I noticed the app in the screenshots doesn't look like native Ubuntu.
There is no such thing as "native Ubuntu" :-). The default widget style of a modern Ubuntu installation is just a GTK theme (which, I think, supports both GTK 3 and GTK 2 -- the two are incompatible, so themes need to implement support for both). You can configure Qt to use the GTK 2 rendering engine, but GTK 2 and GTK 3 look slightly different for reasons that I am entirely unable to convey without an inflammatory post, so Qt (and GTK 2) applications won't look exactly the same as GTK 3 applications.
I am not sure how this is going (this blog post is the only info I can find on it) but they have plans to make a new UI library for Qt that is backed by the platform's native widgets, like AppKit on macOS: