How sound is the Hadith: "Righteousness does not decay, sin is not forgotten, the Requiter does not die; Son of Adam, do what you will, for as you judge, you will be judged"? And is it permissible to write it in forum signatures or personal messages if it is weak?

The hadith (definition) is mursal (with a missing Companion in the chain) and was narrated by Ahmad as mawquf (وقف — stopped at a Companion) from Abu Darda, and there is an interruption (inqita') in its chain. It was also narrated by Ibn Adi as marfu' (مرفوع — attributed to the Prophet) from Ibn Umar, but its chain of transmission contains a narrator whose weakness is unanimously agreed upon. Therefore, the hadith is weak, but its meaning is sound.