will tin signs hung against basement concrete walls rust?

Metal degrades due to physical and chemical weathering. If your "tin" signs have few scratches, the tin or zinc coating and the paints will continue to preserve the metal. Concrete is never entirely dry, and basement walls are likely to transfer moisture from the exterior to the interior. If your basement has high humidity you can mitigate it with a dehumidifier. You can also paint the backs of your metal signs to prevent moisture from reaching the metal. If you have excessive dampness you might consider coating the walls/floor with a sodium silicate concrete sealer.

tin does not 'rust', although it oxidizes. Your rust is iron oxide.

Yes, they will. There is always a certain amount of moisture that penetrates an underground concrete wall.