No. The best place to get help for a toothache is with a dentist. More and more, you will find urgent care dental practices. You may have a significant abscess (infection) at the site and require antibiotics. Seeking pain medication may only mask the underlying condition and create a dependency. Dentists are the best practitioners to handle tooth related issues.
Maybe. If you have swelling, difficulty breathing or an uncontrolled infection and you have no way of seeing a dentist than you must seek emergency treatment. If your pain and swelling is not sever than you can use some over the counter pain medication and see your dentist as soon as you can.
It depends. Toothaches usually develop slowly, giving you time to see a dentist to fix it before it gets too bad (they never get better on their own). Emergency doctors are not dentists and can't fix your problem, but can help under certain circumstances. If you have facial swelling or fever, you have an infection and need antibiotics. Severe pain may require prescription pain meds until you can see a dentist.
Usually Not. Toothaches by themselves are usually not life-threatening unless they are accompanied by significant facial swelling. The danger, of course, is that such a swelling can appear rather quickly and spread into sensitive areas of your face and neck, causing permanent damage, and even restricting your airway. So, while the toothache itself can be very painful, it's the swelling which is most dangerous.