How long should it take for nerves to heal after back surgery?

Depends. This depends on how long & severe the compression was as well as the underlying "health" of the nerve-the age of the person, is diabetes involved, a vitamin deficiency, a prior injury or surgery to that nerve, toxic exposure- all play role in prognosis or ability of the nerve to "heal" over time. For most, pain is usually alleviated once nerve is decompressed, but neurologic recovery is variable.
It depends. I assume you are talking of disc surgery, which the nerve involved. We have to consider two things. How chronic the painwas? How much the nerve injury is? It may take days? Few weeks? It may have residual pain for long time?