Yes. Yes. Herniated discs do heal. Surgery is not a requirement unless you have very specific and obvious complications. Back pain on the other hand may or may not be related to the disc or to its recovery. Disc does not equal pain and pain also does not equal disc.
Yes/No. Surgery will remove the disc so it will not heal normally but can result in reduction in pain and resolving any lasting nerve damage due to the disc herniation. Healing on its own will take time and may keep the integrity of the disc intact which may be the best at keeping the disc as normal as possible. Healing on its own can take up to 6-9 months or longer.