Is it just me, or this really sounds like 'on ciasto gotuje'
I don't think it does. It may sound a bit too much 'en' than 'ę', but not 'ciasto'.
That's what I thought too, but I still have trouble distinguishing some of the different sounds.
Why is "He frequently cooks" incorrect?
Oversight, added now.
And he rarely wears trousers.
What about he cooks regularly
Well, "regularly" can be also "He cooks on every last Sunday of the month", which isn't exactly "often" ;)
How about: "he is often cooking"
Words like "often" shouldn't really be used with Present Continuous.
How about "he cooks a lot"?
That's "On dużo gotuje". I understand those can be very similar, but it's still a different adverb.