Re: ball shoes
It's better but now it seems odd that your title is "a new pair of shoes" but those words don't actually appear in your post! Please take more care in future.
The following are natural and correct:
My father bought me a new pair of shoes.
My father bought me a pair of shoes. (We would assume they were new. People don't generally buy other people second-hand shoes.)
My father bought me some new shoes. (Admittedly, this loses the information that it was just one pair.)
My father bought me new shoes. (Again, this doesn't make it clear that it was just one pair.)