My gross Salary is $ 5000/month
Tax withheld from my monthly paycheck are

Federal tax: $422.92

State of NJ tax: 147.58

Medicare: $ 72.50
Social security: $310.00

Total of all the tax withheld is $953.

In the employer quarterly return how much do tax does he owe, considering I am the only employee for the company.

I heard that Employer pays 6.2% of gross wages as Social security tax and 1.45% of gross wages as medicare (Matching of what employee pays).
So considering he will be filing for 3 months with the gross income of 15000 (5000 X 3)
so the total tax he pay will be 15.3% of the gross salary (15000 X 15.3%= 2295) out of which half of it is already withheld from my paycheck. So he will be liable for 1147.5 for the quarter. I will appreciate if you guys are validate that the above calculation is true. Will this be calculated through form 941?

Your Social Security and Medicare tax calculations are correct.

All he has to do is add the $422.92 that was withheld from your check for federal income taxes to the Form 941, then mail the form in by April 15, June 15, Sep 15 or Jan 15. A similar state form is required for the NJ taxes withheld.

He is OVER the threshold allowed for him to mail in the money on a quarterly basis. That has to be deposited monthly at a federal reserve bank.