I belonged to a middle-class family.

The rest of this piece is in present tense, so this should be too. Talking about your family in the past tense would indicate they are all dead.

There are five members: my parents, my eolder brother and, my sister in law, and I(myself / me).

My father is a verythe most honest person I have ever seen.

"(that) I have ever X" is used for extremes ("most" and "least")

Recently, he has been written(retired?) from the organisation.

Not sure what you meant by "written", possible options:

retired - quit, because he's finishing his career
laid off - the company stopping employing him for reasons that weren't his fault
fired - the company stopped employing him (this used to be more neutral, but since "laid off" has become popular, fired is mostly used when the person was at fault these days)

She takehas more responsibilities than other family members.

I think every mother takdoes this.

My mother is a heartfeltsincere womean who takes any kind of action for her family.

"heartfelt" is applied to actions, not to people

Your mother is only one person, so "woman" instead of "women"

I love and respect her too mucha lot.

"too much" is judgemental, it implies you should not respect her that much.

Last year, I completed my M.Sc in PSHRD from RU.

Generally it's good to explain acronyms when first introducing them when the target audience won't know them (e.g. I don't know what PSHRD or RU are - Msc is a little more self explanatory in context)

FromSince 2018, I started studying at RU and completed studying bmy M.Sc degree.

During my academic year, I would dream of going abroad for higher study.

Therefore, I decided to take an M.Sc degree withhich involved a thesis.

Generally, Msc programs here always require a thesis, is it the same where you're from?

After completing my thesis, I submitted to two or mormultiple research paper ons to journals for publication.

"two or more" is used when the number is unknown, greater than two, but small. However, if you submitted to a small number of research papers, then it's more natural to either give a count (as it's expected you would know if the count is small), or just use something vaguer (like multiple) if you don't want to be specific.

Unfortunately, my father has found out he has a complex disease like diabetes.

And also mMy mother has found analso been diagnosed with another complex disease like heart-attack.

We wouldn't just say "has found" a disease. The options are:

"has found out (she has)" which puts the focus on her and her discovery

or

"has been diagnosed with" which puts the focus more on the medical process of discovering that she has the disease.

Hence, I have decided, I won't go to abroad.

I will stay in BD for the rest of my time.

Again, BD is an acronym that won't be automatically understood by most native speakers.

Now, I am studying PGD in BIM.

And I am eager to launch my career as a HR professional.

I belonged to a middle-class family.

Added ED to the end makes it past tense. You are speaking in present if I’m correct

My father is a verythe most honest person I have ever seen.met

You should use the superlative.
Also you’ve known your father your whole life not just ‘seen’ him, so let it a better use here :)

Recently, he has been written from the organisation.

I don’t understand this ,apologies

My mother is a housewife.

I think every mother takehas this. responsibility

It makes sense what you wrote but it’s not the best english

From 2018, I started studying at RU and completed studying bmy M.Sc degree.

After completing my thesis, I submitted to two or more research paper on journal for publication.

Unfortunately, my father has found complex disease likeallen ill with diabetes.

All the other words are unnecessary

And also my mother has found an another complex disease likesuffered from a heart-attack.

You don’t find a disease you are either struck with it or suffering