Only thing I’d add to what Labrati said, is that it strongly looks like its a case of your camera being unable to acquire focus as opposed to motion blur.
Too see what he said about contrast in action, try to focus on a star at night (almost no contrast) . Then swing the camera and acquire focus on the moon (high contrast). And yes all cameras will struggle in low light scenes like that, often depending on the subject matter forcing the photogrpaher to manually focus…talk about old school 🙂

The other thing to be aware of is motion blur. Even with whats known as a fast lens (f1.8) wide open, that above shot took 2.5 seconds to “expose”…Gather enough light to iluminate the facial features.
Tripods are a must.
One thing you can try given the limit off PnSs being unable to manually focus and to overcome their weaker “AF assist” light is to use a flash light to acquire foucs. While your exposure reading will change once you turn it off, you will if you keep the button depressed maintain focus.