Writinge the words seriously and honestly in the card.

This sentence is incomplete because it's missing a subject. I suggest either "Write the words seriously and honestly in the card." because you are instructing the person how to write or "Writing the words seriously and honestly in the card is important" because you are describing the writing.

Your question makes a recall of my memory to me.

I understand the sentence, but I think it can be written to sound more natural. "Your question brings back a memory.", "Your question helps me remember, "I recall one of my memories because of your question."

A girl moved my heart bywith a simple card with ain the mail.

We awere deskmates when we are studyingied in a junior school.

Because you are talking about a memory, I think the rest of the sentences should be in the past tense.

She iwas a gentle and kind grirl and easy to cry bycried easily because of other’s bullying.

past tense.

I amwas the boy who always againstbroke the rules and iwas naughty, so I protected her every time when she iwas bullied by others.

past tense.

Time goeswent by, and we went to different high schools, and there is n. Nothing special happened beforeuntil I receive a mailletter from her.

I think the sentence is long with because of all the "ands". I suggest splitting it up to make it easier to read, but if you were speaking, all of the "ands" would sound fine.

You got a mailletter from a girl.”

“Who willould write a mailletter to me in this era thatwhen everyone has a phone?” I opened the mailletter with confusion, and I read it.

"in this era" is fine but it's not as commonly used.

We don’t have a chat long time, so I can’t stand myself to sendhaven't talked in a long time, so I had trouble writing this card to you.

I am writing this mailletter with a warm heart.

Although I decided to study hard and do not makeput myself in an embarrassing situations which I need to miss a person every time, I still do it.

I didn't understand this part of the sentence " which I need to miss a person every time", so I recommend removing it. The sentence still makes sense without it.

I guess you have a good academic grades.

AYou put a lot of effort you dinto it every day in your daily life.

I am only a good friend in your heart.

Maybe "I am only a good friend to you", but since this is a love letter. I think "in my heart" works.

To ask how are you now, and what are youyou are doing and so on.

I feelt moved and really appreciated.

past tense