When BTC is traded at a Bitstamp, Mt Gox (or similar) what is the algorithm for matching Buys to Sells? How do partial fills occur?
(2) is the correct answer, the exchange will match the buy order with the lowest sell orders. This is the case with mtgox. Other exchanges should do the same, however it is up to them, hard to give a general answer here, need to look at each one case by case

(4) is specifically NOT true in case of mtgox because they do not act as counter party to any transaction. Not sure about any other exchange, because they all have their own policies.