To what extent and in what ways are Crooks and Curley's wife similar? How are they similar in the category "shattered dreams"?
This question is hard to answer as it is expressed. These two characters do not have shattered dreams. Curley's wife is too young to have had her dreams shattered. Steinbeck does not give her precise age, but from her conversation with Lennie in the barn, as well as from the fact that many of the men call her "jail bait," one gathers that she is still very young, perhaps as young as sixteen. She had hardly had time to formulate any dreams, much less to have them shattered. She is in a miserable place, married to Curley and isolated out in the boondocks, but she is really too young to realize it yet. If she had lived she would probably have run away and ended up in some town or city waiting on tables. She seems to be trying to run away even within the confines of this ranch. She had some vague hopes of becoming an actress, but they were not solid enough to be shattered.
As far as Crooks is concerned, he is a black man without any talents or prospects, living among bigoted whites and not even permitted to enter their bunkhouse. The most he can hope for in life at this period in American history is to hang on to some menial job and to avoid being brutalized. If he lived in a city he would be confined to a black ghetto, but at least he would have friends. Somehow he ended up in this all-white farm country, and he is wise to keep to himself and create his own little world in his humble room. He probably never had any serious dreams to be shattered. In fact, he is probably the most realistic character in the entire cast.