How long do pinched nerves take to heal?

Usually no surgery. Most just get better with time. So anyone can claim a 90% success rate with their care as this is the natural history but lifestyle changes including exercise, smoking cessation and weight control are important especially in minimizing recurrences. Sometimes , physical therapy, activity modifications, medication and epidural steroid injections can be of benefit.
Variable. It depends on what nerve, the extent and duration of the injury, and the degree of decompression achieved. If surgery was needed, then the presence of scar tissue can also play a role in the prognosis.