"is wearing", yes.

"wears", not so much. It's a habitual action, not necessarily performed right now. "Ma na sobie" usually is used to describe what a person is wearing at the present time, "nosi" can be used for both.

The grammatical case. "Skarpety" is the Nominative plural, as well as the Accusative - and this is the case used here. "Skarpet" is Genitive plural. See the declension here.

Plural and singular

The plurals are 'masculine personal plural' and 'not masculine-personal plural'.

Also no, it's not masculine anyway. "skarpeta" is feminine. But even if it was masculine, it doesn't refer to a man, so it's still the second plural.

It sure is "on".

Only "skarpety" was taught in this course, so "skarpetki" can just be an accepted option. I'd normally choose "skarpetki", but if there are 'large', then actually "skarpety" do indeed sound better to me.