Potential project: Wireless Security Camera with the Arduino Yun
1) Having it connected to a PC is not necessary, an eyefi SD card is a great idea but you already have wifi onboard, why would you need another one?

2) The power source is the computer. But again, you can battery power the board. I don't know where that 6AA batteries comes from but that's probably too much, the PC provides 5V through the micro usb, why would you need 9V? Depending on how much autonomy you need, how big the batteries can be and how much money you can spend an appropriate battery solution might (or might not) be found.

3) That just depends on what who's answering likes more, I've used the raspberry but maybe someone else likes arduino more.