I wasToday I have been studying English for tomorrow’smy placement test todaymorrow.

My college is starting againresuming classes tomorrow even though the coronavirus is still going around in Japan.

My college is starting again tomorrow even as the coronavirus is still goingspreads around in Japan.

The other corrections are good, I just wanted to give an alternate way to write it.

My college is starting again tomorrow even though the coronavirus is still going around in Japan.

I really cannot believe this...!

Today, I was studying English for tomorrow’s placement test today.

You can also say:
I was studying English for tomorrow’s placement test, today.

I think my first correction is the most clear and natural sounding. Otherwise, it may be confusing.

My college is starting again tomorrow, even the cough Coronavirus is still going around in Japan.

Even though is a common group of words. Coronavirus is a proper noun.Because of this, the first letter is capitalized and you remove the word "the".

You could also say "even though the virus is still..." because virus is a noun.

I really cannot believe this...!

If you want to add emphasis, you can say something like:

"I cannot even believe this!"
or
"I cannot really believe this!"

But the first sounds more natural.

I hopeHopefully, the virus goes away soon.

Let me clarify, the above sentence you wrote is correct! The correction I made is a suggestion to help sound more natural and add more complexity to the sentence.