I just put my wallet.dat file into a new Bitcoin-qt installation. It's taking quite awhile to synchronize with network. Am I able to send my "unconfirmed" bitcoins to someone now or do I have to wait until they're confirmed?
You can absolutely start sending now, as long as you are positive that no transactions have been made with that wallet since the time it was copied from the old installation. Be aware that because there is a lot of traffic going between your node and the nodes you are connected to while you are syncing, the transaction may take much longer to be broadcasted. In the past, it's usually been about 30 minutes for me, but your milage may vary.