What is the grading of the Hadith: "There is no hour that passes over the son of Adam in which he does not remember Allah except that he will regret it on the Day of Resurrection"? Is it legislated to set a clock alarm to remind one to perform Dhikr every hour, and is it permissible to inform others of this action?

The hadith (definition) mentioned in the question is very weak. There are other hadiths regarding the virtue of dhikr (remembrance of Allah), among them the hadith of Mu'adh (may Allah be pleased with him): "The people of Paradise will not regret anything except for an hour that passed them by in which they did not remember Allah the Almighty." This hadith was graded as weak by Al-Albani. However, Al-Albani authenticated the hadith of Abdullah ibn Amr (may Allah be pleased with them both): "Indeed, for everything there is a polish, and the polish of the hearts is the remembrance of Allah. And there is nothing that saves from the punishment of Allah more than the remembrance of Allah." The remembrance of Allah the Almighty is among the best acts of worship, as stated in the hadith of Abu Darda (may Allah be pleased with him): "Shall I not inform you of the best of your deeds and the purest of them in the sight of your King? And the highest in your ranks? And better for you than spending gold and silver? And better for you than meeting your enemy and striking their necks and them striking your necks?" They said: "Yes, indeed." He said: "The remembrance of Allah." There is no harm in setting an alarm to remind one of dhikr, or in directing others to do it, as it is a form of inviting to goodness.