describe the "caste" system in the new world, why is it important?
The 'caste' system is reminiscent of the caste or class systems in India (I'm not sure if it still exists?
) which essentially means that people are categorised depending on a feature (or lack thereof). Feudal England was also based on a caste system - the monarch was the top 'caste' or class, and the roles filtered down to the humble peasant.
In BNW the caste system is denoted by the names 'Alpha', 'Beta', etc. and, similar to the caste systems of the political systems mentioned above, you're born into a caste rather than working your way up the ladder (which is the case in our society now.. theoretically). In BNW the caste system is generated by the government to control the people - it is a form of population control. Also, it is interesting to note the merging of elements of old/new cultures in BNW - the feudal system has reemerged in the BNW.
To answer this question properly you'll probably have to research caste systems.
what is it hypnopaedia and what is its importance to the new world?
Look up the definition of hypnopaedia. You can probably figure this out from its context in BNW anyway. It's used as a method of controlling the people, since they are hypnopaedically conditioned with an attitude towards life. You can probably figure out yourself why THAT is important - remember the BNW motto, "Community, Identity, Stability" (believe me, you don't forget it!)
Who is mustapha mond? how is he important in helping us understand the beliefs of BNW>?
AFAICR, Mustapha Mond is one of the few World Controllers. If THAT title doesn't tell you what he does, then you're going to have trouble with the rest of this course
Examine his role in the first few chapters.. what he says about the society (when he's talking to the Alpha students). Later in the novel we're exposed to more of his role in the society and how he has been affected by the societal rules and structures.
Hope that all helps. If you're having trouble, try to look at the specific parts as relative to our society (or the past) - they give you an idea of how they were used previously and why they were stopped.