What is the difference between a market and limit property in the MTGox API?
A limit order is an order to buy or sell at a specific price or better. As in "sell these coins if I can get at least X USD per bitcoin."

A market order is an order to buy or sell at the best available price. As in "sell these coins for whatever people are willing to pay right now."

Not 100% sure about this, but I believe mixed_currency means the buyer and seller are using different currencies. If you buy bitcoins using EUR from someone selling for USD then MtGox will do a conversion.

And yes, the best view of the market would be with all trades included.