Has the BitForce Bitcoin Miner be connected to a PC all the time? When the BitForce Bitcoin Miner is mining, does it have to be connected to a PC all the time?
Yes. Mining devices such as this are merely highly-specialized processors that communicate with a computer via serial over USB. The computer is necessary in order to tell the device what to do, and to get its result to post to the mining system (i.e. a pool or bitcoind).