Do rib fractures heal by themselves or not?

Yes: Only the extremely rare fractures that involve multiple segments of the same rib or adjacent ribs need surgical repair. Even many of these will heal by themselves.

Yes they will: As with most other broken bones, rib fractures will heal on their own in the vast majority of instances. There may be situations where a surgeon needs to fix the broken ribs (if multiple ribs are broken in 2+ spots each), but that is more for the breathing, as the surgery doesn't make them heal - your body does.

Rib fractures : Simple rib fractures are treated conservatively with pain management only. Certain rib fractures that result in breathing difficulties and / or relentless pain are treated surgically. I use titanium plates to repair the chest wall.