To what extent does a costom mouth guard cost?

It varies. The fees that dentists charge for mouth guards varies from office to office. There is also a difference between an athletic guard and a brux guard. It's best to discuss this with your dentist.
Depends. Depends on type, materials, upper/lower/or both, region of the country, etc. You want the best mouthguard you can have custom made, because the cost of a mouthguard as considerably less than having to deal with a broken or destroyed tooth, or a concussion. Ask your Dentist for more information.
All Depends. Custom mouthguards can be priced from a few hundred dollars and upward. Custom mouthguards require impressions of both upper and lower dental arches and a wax bite registration. After tihe initial fabrication, the mouth guard must be fit in the mouth and then have the bite adjusted. This takes time and expertise. I'd expect to pay at least $500.00 for custom mouth guard.