Welcome to gyne.org, HHH.
Yes, usually, surgery is the only way to correct gynecomastia after it has been established, especially if it's been there for years. One surgery is all most people need, but if the condition is severe, it's possible that the surgery might have to be done in stages.
It's very important to realize that the first surgery is your best chance to get the best results. So it is very important to choose your surgeon wisely. Go to a board certified plastic surgeon who has a wealth of experience in correcting gynecomastia. Not all plastic surgeons have experience at correcting gyne, so preferably, go to one who specializes in it and performs many each year. Also, before choosing a surgeon, look at many before/after pictures of their patients, because that's the results YOU can expect. If you don't like what you see in the pictures, go to another surgeon. Also, ask the surgeon to show you pics of other guys who had gyne similar to yours. This gives you a good idea of what you can expect from your surgery.
If your gyne has "burned out" and is no longer active, then there is little chance the breast tissue would grow back after surgery. But it can (and does) happen if guys elect to have surgery too early and their breasts are still in an active growing stage. If your condition has been stable for a couple of years, it should be fine to have surgery without the fear of anything growing back.
As far as when you can go out in public, that really just depends on YOUR situation. There are many variables involved, like how severe your gyne was, what all was involved in correcting it, etc. But usually, a few months is required for most guys to feel good about going out in public without their shirt.
Scarring depends on the same factors as above. The severity of your gyne and how much was required during surgery will determine your scarring. But most guys are happy with the degree of their scarring, as the way they look after the surgery is typically soooo much better than what they looked like before. The guys that usually complain are the ones that had mild gyne from the start, but a bad surgeon made their chest look worse than it looked before the surgery. Again, it is very important to choose a surgeon with LOTS of experience at correcting gynecomastia. No surgeon likes going in to clean up someone else's mess, and the chances of optimal results go down with subsequent surgeries.