Maybe back then I was just severaln or eight years old when I tried to make noodles.

“Several” implies that you feel the number was not small, which isn’t what you want to say here. Since you say below that it was in 2nd or 3rd grade, I changed it to “seven or eight years old.”

suggestion: I was maybe seven or eight years old the first time I tried to make noodles.

One day, my mom went to the fields to do farmers' work (or: went to work in the fields), and only meI was at home. (or: and I was home alone)

When my mom wentcame back home, I told her that I had already cooked the noodles for her.

“Came” because you were already at home, so she came toward you. The usage of came/went is similar to 来/去.

Maybe back then I was just severala few years old when I tried to make noodles.

Typically in English we say either "a few years old," "young," or a specific age (example: I was eight years old when I tried to make noodles). "Several" works as well, but these options may help you sound more fluent.

One day, my mom went to the fields to do farmers' work, and only meI was at home.

Here, you were doing the action of "being at home", so you would use "I" instead of "me."

I often saw that my mom often made noodles, so I thought I should be able to make them too.

Only need "often" once.

I thought it would be a big challenge for me because I haved never done any cooking.

Past tense - "had" never. You could also add "before" at the end of your sentence to give some more detail, but this is not necessary! (Example: I had never done any cooking before.)

Then, I took a certain amount of wheat flour and sweet potato flour, mixed them, and made them into a dough with water.

Afterwards, I flattened the dough thin enough with a rolling pin, folded it, and cut it into noodles.

Because I was just a kid, and not that strong, and that was the first time I made noodles, so the noodles were not thin enough and long enough.

By saying "thin and long," the word "enough" would apply to both.

Then I boiled the water in the pot and put the noodles in to cook ithem.

Noodles is plural. You were cooking more than one noodle, so you would say "to cook them."

When my mom wentcame back home, I told her that I had already cooked the noodles for her.

If you were already at home, it sounds a little more natural to say "came back home" here.

It was the first time I did something to help my family when I was in grade two or grade thresecond or third grade in elementary school.

In English we typically say "second" rather than "grade two," but this is just to speak more naturally. Even saying "grade two," you would be understood by English speakers.