Is the Udhiyah that the father bought for his son without his knowledge of the sheep's form or price, except after the sale, then the son returned the amount the father paid for him, valid and does it avoid the suspicion of Gharar (uncertainty) in the sale?

There is no gharar (definition) (excessive uncertainty) in the aforementioned sale. You authorized your father to make the purchase, and he bought a specific sheep for you at a known price. Therefore, the sale is valid, and the udhiyah (definition) (sacrificial animal) is valid, God willing.