Only a few US issues have naturally occurring straight edges as part of the printing process. These straight edges are sometimes reperforated to make the stamp appear to have perforations all the way around to increase its value. Straight edge copies sell for about 50% of normal copies with full perforations.
Just because a stamp issue doesn't have naturally occurring straight edges, those stamps may be reperforated too. Three reasons that I can think of for doing this are to: 1. improve the centering of the stamp or 2. to remove some damage like ragged perforations or a thin along the edge of the stamp, or 3. to change the appearance of the stamp such as adding perforations to an imperforate stamp to make it into a rare coil.
Reperforated stamps can occur on almost every US issue. You should check the perforations on all stamps.
Gum is added to a stamp to increase its value. Mint stamps with full original gum sell for more than stamps that are missing some or all of their gum.
If a stamp is hinged, it may still be regummed. Regummed stamps have been around for a long time. And along the way, the stamp may have been hinged by some collector.
It's true that hinged stamps are worth less than never hinged stamps. But just because a stamp is hinged doesn't mean that the stamp has original gum. When checking your stamps for original gum, you should check every stamp including the hinged ones. They may have been regummed too at some point in time.