Is it bad to keep the special nose piercing stud in longer than a week?

Well if the piercing was done by a professional body piercer the nostril stud can be left in, it doesn't need to be removed. But if the piercing was done by a hack with a piercing gun then you need to go see a professional body piercer and get some real good quality body jewellery for the piercing you have. Piercing guns are not designed nor intended to be used on anything other than ear lobes, most health regulations consider it's use for other locations a violation of the health act. Piercing gun salons are not licensed for body piercing so there scope of business is restricted to ear lobe piercing only.