Are the Whites' three wishes granted, and do they get what they really want in "The Monkey's Paw" by W. W. Jacobs?

The Whites’ three wishes are granted, but not always in the way that they wanted.

The Whites do not really take the monkey’s paw seriously.  The Sargent-Major explains the paw is dangerous, and says they should just throw it in the fire. He even tells them the third wish of the last person to have the paw was for death.

The Whites do what most people who are presented with a magic token that grants wishes would do: they wish for money. Mr. White says he is happy and does not want anything, but his son encourages him.

"If you only cleared the house, you'd be quite happy, wouldn't you?" said Herbert, with his hand on his shoulder. "Well, wish for two hundred pounds, then; that'll just do it."

Herbert winks at his mother. He clearly thinks this is just a lark. None of the Whites realize they have made a terrible mistake. As everyone goes to bed, Mr. White thinks he sees monkeys in the fire and is disturbed.

The Whites get their money, but not in the way they wanted it. Herbert is killed in a terrible accident at the factory, and his employer compensates the Whites with two hundred pounds. This is obviously not what they wanted. They would much rather have their son than the money.

Mrs. White is overcome by grief, and wishes again on the paw. This time, she wishes for her son. 

"No," she cried, triumphantly; "we'll have one more. Go down and get it quickly, and wish our boy alive again."

The man sat up in bed and flung the bedclothes from his quaking limbs. "Good God, you are mad!" he cried aghast.

Mr. White is opposed to using the paw again. He knows things did not turn out well the first time, and is beginning to believe the paw is actually cursed. His wife is desperate with grief, though. When there is a knocking at the door, he is horrified. He worries what condition their son’s corpse will be in since he has been dead ten days.

Mr. White decides not to wait to see what is at the door. He makes the third wish, and the knocking stops. I guess you could say that this was the only time the Whites got what they really wanted. Mr. White wanted his son to rest in peace, not be some horror they could not face.