Does smoking cigarettes make you have to urinate more often?

Unlikely. Smoking cigarettes is a risk factor for bladder cancer. It should not make you urinate more often. However, the breakdown products of smoking can cause bladder irritability and possibly cause urinary symptoms although this is not common.
Possibly. Nicotine makes you more likely to poop. Its effects on urination hasn't not been as well described but i would not be surprised.