Yesterday, I talked toold the headmaster that I wanted to quit.

She asked me the reasonwhy.

I think it's much more common to say, "She asked my why". I think what you wrote is correct though, just not as common.

I told her that I have stoo many exams in the followupcoming days.

You could change "have too many exams" to "had too many exams" if you have already taken the exams. If you haven't taken them yet then you can leave it as "have".

She said, " I would have never thought that your ambition ofdesire to studying abroad iwas so strong."

I changed it to something that sounded a little more natural to me. I think you could still use "ambition" instead of "desire" in my corrected sentence.

As far as the beginning of the quote, there are a couple options here. "I would have never thought..." or "I never thought...". I struggled to decide which one to use, but they're both correct.

She also wondered why, especially concsiderning the globale pandemic wais so severe, while that in China was far more in other parts of the world while in China it's much better.

I know what you're trying to say so I changed the sentence to try to make it a little clearer.

"Becasuse if I don't act now, I will only get older, and things will beget more difficult," I replied.