Not good, but OK. This shouldn't have any untoward effects on your long term results. Touch base with your surgeon. Don't blow the nose, and avoid any Aspirin or Aspirin related products unless recommended by your surgeon. An otc decongestant product should be fine to help you if you don't have any other medical issues (like high blood pressure). Nasal saline spray is also good to use.
Not really. A cold will not disrupt the healing process, but you must be careful not to blow your nose. If you develop a fever or there are other concerns with healing i would direct it to your doctor.
Not usually. Infection after rhinoplasty surgery is rare but many surgeons routinely place their patients on antibiotics as a precaution. These antibiotics however will not treat or prevent a viral infection like a cold. You may however just be having normal swelling inside your nose - which may feel like a cold. In any case it is unlikely that this will adversely affect your outcome.