I'm sort of new to the world of Bitcoin, so excuse me if this is a stupid question:

I'm looking at this exchange bid/ask price and I've got this bid to buy. Its a little low, relative to the current exchange rate, but I notice that there are no takers. There's zero volume and no one will take me up on this offer.

Is volume that low?

Also, how do we know the exchanges themselves aren't manipulating prices?

What do we know about how these exchanges operate or about how this prices get determined? Are there currently offers out there at my price that are not being executed because the exchange operators have some sort of interest in seeing exchange rates set an artificially high price?

We don't know, do we?