A.) Forecasting is the science of predicting future outcomes. In business, it applies to the future of a business, product, or industry. It's extremely important for a business to do proper forecasting before developing new products or product lines, lest you spend a lot of time and money developing a product that fails in the marketplace. An excellent example of a failure in forecasting is New Coke.
B.) This question sounds like it's looking for types that are given in your textbook somewhere. However, here are some ideas:
From wikipedia (since their description was concise and well written):
Product forecasting is the science of predicting the degeree of success a new product will enjoy in the market place. To do this, the forecasting model must take into account such things as product awareness, distribution, price, fulfilling unmeet needs and competitive alternatives.
Trend estimation is the application of statistical techniques to make and justify statements based on trends in data. For example, trying to discern if the trend of a certain industry's expansion will continue, level off, or actually reverse itself.
Technology forecasting is forecasting the future characteristics of useful technological machines, procedures or techniques.
C.) Again, this question is probably looking for information already given to you in the textbook or assignment.
I'll take a stab:
1.) Analyzing the methods used by similar successful companies, and modifying them for their own business plan.
2.) Try several, and see which method work best with the available data, and which methods seem to produce the best results (trial and error).