“Is it bad to drink coffee before the dentist?”

No you can have your coffee. If you are concerned about bad breathe, you could brush your mouth before the appointment.

If you have a history of being difficult to get numb and you are going in for something other than a routine cleaning I would skip the coffee, otherwise you are fine.

Don't worry! Drinking coffee before visiting your dentist is not a bad thing. However, it is the quantity and what you put inside the coffee that matters most. For example, someone who drinks more than 3-4 large cups of coffee a day is not good. Someone who puts a lot of sugar in their coffee is bad for their teeth. Someone who constantly sips on a sugar-loaded coffee around the clock is bad for their teeth and their health. Caffeine is a stimulant. Our bodies will develop tolerance and get use to the caffeine over time. Our body will crave more caffeine. You heard the story that some people have to drink at least 4-5 cups of coffee a day. If not, their body will develop withdrawal syndrome such as trembling and nervousness. For teenagers, if you have enough rest and good hours of sleep at night, regular exercise, there is no reason to drink coffee to "keep yourself awake" during the day. Having said so, if you have to stay up late studying and preparing for your final exams, it is okay to drink some coffee once in a while.
Hope that answer will help!

Teeth can stain

Only if you want to have coffee breath.

No. It is fine.

I am sure your dentist has seen far worse problems than people drinking coffee, so it should not matter to him or her.