Q. Will the payment made by father in advance directly to the university be considered as Gift to me?
A. No. Tuition payments made directly to a college are not considered gifts for tax purposes (the education exception). Furthermore, if you are your parent's dependent, the money is considered support not a gift.
References: https://www.thebalance.com/what-gifts-are-not-subject-to-the-gift-tax-3505684
https://www.schiffhardin.com/insights/publications/2018/faqs-on-the-use-of-the-gift-tax-medical-and-...
Any amount reimbursed by tax free employer assistance is not eligible for a tuition credit or deduction. If the employer reimbursement is treated as taxable income, then the tuition is eligible for the credit or deduction. Employers are allowed to pay up to $5250 of tax free tuition, for an employee. So, it depends on how your employer handles the reimbursement (and whether their tuition reimbursement plan meets IRS rules). The fact that your parent made the original payment is not relevant.
