Shifting poorly in middle gears + odd grinding

So my dad doesn't use his newish bike much, but developed an odd issue. The middle gears seem to skip, which I tried fixing my using the barrel adjuster to no avail, as well as tightening the cable itself on the smallest cog.
Additionally, the chain seems to rub on the next gear when in the middle gears, and you can see in the picture why this is.
What would cause this? The wheel is seated properly. I do notice a slight wobble on the cassette but that's relatively normal, no?