Two verbs and one adverb in a sentence

Hello everyone.

I am curious about adverb use in a sentence with two verbs.

Examples;

1-) I am good at cooking quickly.

I mean, I can cook quickly. But I think, the sentence is incorrect. Because “quickly” doesn’t belong to “cooking”. The true one can be:

I am good at quick cooking

or

I am good at cooking in quickness

—

2-) I gave up studying continuously.

I mean, I had studied continuously and I gave up it. I think, it is also incorrect because of the same problem. “Continuously” belongs to “gave up”, not “studying”

The true one can be:

I gave up continuous studying

or

I gave up studying in continuity

—

3-) The first rule of being prepared carefully for the exams is to sleep enough.

or

The first rule of carefully being prepared for the exams is to sleep enough.

or

The first rule of careful being prepared for the exams ...

Which ones are correct?

Thank you very much in advance.