What happens to cash used to buy bitcoins? Are there any requirements to Bitcoin exchanges [USD/EUR/etc], as to for what the [USD/EUR/etc] may be used? Or is the [USD/EUR/etc] received property of issuer of bitcoins?

Unfortunately, this is not decribed anywhere.
Bitcoin exchanges, like stock exchanges, act as a middleman for people that want to trade bitcoins. They do not sell/buy their own bitcoins or US Dollars.

Suppose that I have 10 bitcoins and I want to sell them at $5 each. In order to do that, I can use a bitcoin exchange and put a sell order at $5 for 10 coins. This is a way of "announcing to the world" that I will sell 10 coins to anyone who is willing to pay me $50. If you want to buy them, just login to the exchange and put a buy order at $5. The exchange will match our orders and I will receive your $50 and you will receive my 10 bitcoins.
When a buy order matches a sell order, a trade is made. This is how the bitcoin price is defined.

Now suppose that you want to buy bitcoins, but you are only willing to pay $4.9 for each bitcoin. You will put your buy order at $4.9, but it will not match mine because I only sell if you pay me $5 per coin. The amount of pending orders defines market depth. 

For example, you can see here the market depth for MtGox. The bids table show the price people are willing to buy at and the asks table show price people are selling at. MtGox Live is also a nice way to visualize these concepts.

Note that bitcoin exchanges charge a small fee (currently around 0.5%) each time they match an order. So in the previous example I would receive $49.75 and you would receive 9.95 bitcoins. The rest is kept by the exchange for their services.