Are the Mt.Gox markets for different currencies completely separated?
There is only one order book in MtGox. Orders aren't segregated by currency, rather, all prices are relative to the currency with the highest volume (based off The European Central Bank's daily rates). In their own words,


  For example, if a buy order for bitcoins is placed in EUR, the order can be executed against another user selling bitcoins in any currency and not necessarily only against another user selling bitcoins in EUR.


That said, wallet currencies are completely separate. There's no converting between them unless you're transferring that value via bitcoins themselves. For example, you can buy bitcoins in a EUR wallet with EUR, transfer them to a USD wallet and sell them in USD. Of course, you have to consider how you'll withdraw the resulting currency.