How long does it take to correct an underbite?

Depends . It all depends upon the nature of the underbite and the severity. As adults, true, severe skeletal discrepancies are usually dealt with by either extractions of teeth to hide or camouflage and/or orthognathic surgery. The only way to determine the severity of your situation is with an appointment with your orthodontic specialist.
Varies. There are different degrees of underbite, so it will vary. That said, an "underbite" (also known as a class 3 maloclusion) is one of the more difficult maloclusions to correct, so you will likely in for at least 18-24 months, possibly more.
It depends. It depends on whether you're discussing orthodontic treatment (braces) or corrective jaw (orthognathic) surgery. With braces, depending on whether teeth are extracted, it may take 18-24 months, if it's done right. Avoid speedy braces! if you're talking about surgery, it takes about 3 hours, but is still done in conjunction with orthodontic treatment, so the total treatment time is about the same.
Ask an Orthodontist. It took you 37 years to create your malocclusion. Please don't expect a quick fix. An Orthodontist can determine whether your malocclusion is dental, skeletal, or a combination of the two. Orthodontic care alone may camouflage your underbite, but a combination of braces (not Invisalign) and surgery may be required for optimum treatment. Please see an Orthodontic Specialist.
Depends on severity. Could range from as little as 6-9 months (rare) to 24-30 months depending on spacing/crowding and the severity of the underbite.