I have a few suggestions:
He is a no-nonsensestern man
He rarely jokes with others jokingly , even with me,who is his daughter.
He is an excellent leader in his company and a strict father for me.
I think this statement would be stronger if you gave a specific experience or example that shows his excellent leadership. :)
He always requires me to do every thing wholeheartedly and never allows me givingto give (do you see why?) up until to the last.
Stern as he is, (Remember to put a space after your commas) father is full of affection to me
The above italicized phrase seems a little awkward to me. I'm not sure - you may be right - but I'd recommend "father shows affection towards me" or "father is affectionate toward me"
Not only does he encourage me to insistpursue my dream but he (You need a subject here because you put "Not only" before the subject) also lets me learn to enjoy the process of striving for it.
I benefit from the communication with my father very much.
What communication are you talking about? Be sure to expand and give examples. This will make your essay much stronger.
With his worthy advices I could increase myself gradually.
What do you mean by "increase myself?" Could you explain this? Then maybe I can find the right phrase. :]