Can cystoscopy cause urinary incontinence in women?

No. Cystoscopy is simply a technique to view the inside of the bladder with a video camera. It would not cause incontinence but may be part of the evaluation of incontinence in some patients.
No. Not usually. Every procedure has risks. Rarely you can get a temporary incontinence or urinary retention from cystoscopy. Even more rarely could damage be caused to the urethra that would cause a permanent incontinence.
Generally no. Cystoscopy can be used in the evaluation of urinary incontinence, but is not generally known to cause incontinence itself.
Usually no. It should not. It is extremely unlikely to cause damage with the cystoscope to the bladder in the hands of a trained and experienced urogynecologist or a urologist.