Is it safe to delete bootstrap.dat.old? Is it safe to delete bootstrap.dat.old? Because my bitcoin-qt is using the internet to synchronize right now ("Importing blocks from disk." stage has finished). But I still am not sure.
Yes, it is marked .old to indicate it is safe to delete. The blocks have been copied and  imported into the main blockchain that you store. The process took time because the client was verifying the blocks.