Is it safe to charge my iPhone using my lightning cable and someone else’s adapter at the Airport? The airport has USB ports that say they are for charging and I don’t know how to tell if this situation is safe. 

Is it safe to charge my iPhone by using USB connections that are behind a wall plate in public?
Being that its the airport, you're most likely safe, but good rule of thumb is try to avoid free charging stations and use wall outlets wherever possible. Your iPhone can have malicious data transferred in and out of it if one of the ports has been tampered with.