The reason is because there were so many problems in withdrawing from Mt Gox.
Yes. It is difficult to get dollars out of MtGox, so most people buy bitcoins and withdraw those instead. That means that there is a high demand for bitcoins and a low demand for dollars, which leads a higher rate for bitcoins than other exchanges where dollars can be withdrawn.
It's to entice more customers I guess.
No. Mtgox does not control the prices on their exchange