I would not clip your bird wings, the cats are a big reason, however they are not my only reason and therefore I do not believe in clipping a birds wings unless there is a valid medical reason for doing it.
As for the bird flying into mirrors and/ or windows, your bird will quickly learn where they are and avoid flying into them. Now you do have a cockatiel and they are a bit more prone to panic attacks than any of the parrots that I have and for this reason I would consider putting up some sheers on the windows. I would also place several items in front of the mirrors, if possible, so the bird can recognize that there is a mirror there, of course sheers would also work, but so would a couple of perches or ropes (sisal, would be my rope of choice).