I walked a long distanceway with my aunt to go shopping and to getting exercise.

After we came back home, I ate caurry and rice , and then cake.

After dinner, my friend helped me to do English homework.

My English homework was watching a video/videos about coronavirus and answering questions.

IThey/he/she spoke fast, so it was difficult for me to understand fast speaker.

I thought again my English skillevel is low level.

I walked long distanceent on a walk with my aunt to go shopping and getting exercise.

"I walked a long distance" is okay too. I just read a newer post of yours, and it seems like you walk often. So I think "went on a walk" or "went for a walk" sounds the most natural.

In the same way you say "go shopping," you can say "get exercise." You can even leave out "get" and it will sound natural:
"... to go shopping and exercise."

When you use "get", the word "exercise" is a noun. If you don't use "get," the word "exercise" is a verb.

After we came back home, I ate caurry rice and cake.

In Japanese, "curry rice" is spelled with「カ」, which I think is where your "a" in "carry rice" came from. It's just a typo or spelling error :)

In English "carry" is a different word -- a verb.

After dinner, my friend helped me to do English homework.

It was difficult for me to understand the fast speaker.

"speaker" is a singular noun, so you need to use an article before it.

I thought again that my English skillevel is low level.

There are many ways to say the same thing. What you said was not wrong, but it seems a little unnatural.

My aunt and I walked for a long distance with my aunt to go shopping and to getting exercise.

you can use either to go shopping and to get exercise or say going shopping and getting exercise. The verbs in a sentence must be of the same form

After we came back home, I ate carry rice and cake.

Your sentence is grammatically correct , but writing I ate carry rice and cake for dinner improves the flow of the paragraph

My English homeworkIt was watching video about coronavirus and answering questions.

It was difficult for me to understand the fast speaker. or It was difficult for me to understand fast speakers.

I thought again my English skill is low level.