family with six members
The reader will automatically count your parents as a set of 2 persons. The rest of the family members need to be indicated by number as well. How many brothers? Sisters? Are there extended family members? This reference needs to have better clarity.
My father was teacher
You forgot to use the connecting word "a" in reference to the former occupation of your father. You remember to use the connecting word for your mother though. You cannot use the connecting word intermittently.
I am the smallest of
Smallest refers to height or size. Perhaps you mean "youngest" in reference to your age ranking in the family?
My brother is computer engineering
This your brother's occupation. The person who works in this field is known as a "computer engineer". That is the professional description of what your brother does for a living. The same error exists for the reference to your sister's job as an engineer.
my first sister