The glow plugs remain on for a period of 1 minute once the engine has started. This is quite normal. The GP light on the dash should not be lit.

A lit glow plug light on the dash after the engine has started signifies that one or more glow plugs (or associated circuitry) is faulty.

The relay is a simple circuit, before you consider replacing it open it up and check that there are no obvious faults, like a melted fuse, blackened component, or dry joints: