Tracing a gun's serial number through the ATF to see if it was involved in a crime is only permissible for law enforcement agencies involved in a bona fide criminal investigation where a gun is recovered or suspected to be involved.
Get a notarized bill of sale for any gun you purchase so you'll have some protection if the gun is later identified as stolen property.
People who lose their guns' serial numbers won't be able to report them on the sites. The sites' information comes from citizens reporting their stolen guns. Not getting a hit doesn't mean the gun isn't stolen, however. Check the serial number online through HotGunz, Stolen-Property or other stolen firearm sites.
If the sale is illegal, chances are the gun is too. Not all states allow private individuals to sell firearms without going through a licensed firearms dealer.