I think you can spend coins without waiting for them to be confirmed.. 
Yes, but the client won't let you send transactions if they include inputs that are less than 6 blocks deep, unless those same inputs are change to yourself from a previous transaction.
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The next receiver would then have to wait for both transactions to confirm.
Yes, he would.
EDIT: Although the client might appear to let you send quicker than this, because the client (by default) chooses from the oldest of it's eligible transactions to use as inputs to a new transaction. So if you have many transactions of various ages, the client generally attempts to consolidate the oldest transactions. This behavior is beneficial to Bitcoin in general, in the sense that those older transactions could then be pruned from the blockchain by any client that desires to do so.
