Well, as I said, they pay things that are medically neccessary. And dental problems are medically relevant - very relevant even. A whole plethora of illnesses can origin from dental issues.
At the end of the day, its depending on the doctor/dentist statement if something is deemed "medically neccessary" or not. If its confirmed, all treatment is covered by the health service, also dental surgery and whatever else. Only prothesis is only covered partially. And depending on what type of prothesis you want, that can cost you a fortune.
About the pain... its not the worst possible pain, I guess. The weird thing is, you usually dont feel much pain during the treatment - it sets in when you are back home and the anestetic wears off. But they will probably give you some pain killer for that.
Oh and a tip: get something ready that you can eat without chewing, like soup or jello or pudding. But not acidic and to eat cold, to avoid bleeding.