Today's examination whas finished.

Looking back, I feel like I didn't accomplish anything this year.

I feel like vast and hazy.

Time is so fast.

This is good! If you want to sound more natural, Americans tend to say "Time passes so quickly" or "Time goes by so fast" rather than just "Time is so fast."

Today's examination was finish, I reflected on my year.

It seems like by "examination" you might mean something more like "reflection?"

In English, "examination" means "test" and usually has an academic connotation. Athough it can sometimes mean "investigation" (to literally look closely at something in order to learn something), we usually use "reflection" when we talk about figuratively looking at something (for example, we examine ourselves or we examine our accomplishments).

You could instead say "Today I did a reflection" or "Today I reflected."

I feel like vast and hazy.

Time is so fast.flies.¶
I agree with @JoeTofu

Today's examination was finishis over.

We often speak of something being "over" when it is finished or done. It works well here, I think. It conveys the feeling that the exam is behind you now and part of the past.

I feel likeMy impression of the year is vast and hazy.

I'm guessing that you mean that the year seems vast and hazy as you look back. I suggest "impression" to reflect this is how it seems.
(Other people have interpreted this sentence differently, and I wanted to offer another interpretation.)

Time is so fast.

Suggestions:
Time passes very quickly.
Time flies.

Today's examination was finish.ed.

I feel likeEverything feels vast and hazy.

I’m guessing this is what you mean.

Today's examination whas finishbeen completed.

IMy feel likings are vast and hazy.

Not quite sure of the sentence

Today's examination was finished.

I feel likeEverything seems vast and hazy.