Cheese 101 by Rats.
No, no, no you can't make cheese using brewers yeast. Well you probably could but its not going to be very good.
Cheese is made up of the milk solids from milk, primarily protein and fat. The protein needs to be extracted from the milk through coagulation of the protein portion, with what's left over mainly water, lactose and some fats reffered to as whey. Now there are two ways of coagulating milk, using an ezyme such as rennet or through acidification of the milk to its isoelectric point of pH 4.6. Now there are also two ways of reaching the isoelectric point that is through direct acidification such as adding vinegar or similar acids which when simply added to skim milk can produce a quite aceptable ricotta or through the addition of lactic fermenting bacteria such as our good friend mentions above the good old lactobacillus strains. These bacteria will convert lactose to lactic acid and thus lower the pH. Most cheese types use a combination of rennet and lactic fermenting bacteria in their manufacture, not brewers yeast.