Are the aforementioned sayings—such as "Indeed, beauty is a sound heart," and "Indeed, the one who remembers his Lord and the one who does not remember his Lord are like a good tree," and "The date palm is the grace of Islam," and "Calamity is a test from Allah for His servants"—Prophetic hadiths?

The written sayings are not prophetic hadiths nor are they narrations from the Salaf. Therefore, it is advised to abandon them and not to worship through them as a form of dhikr. It is preferable to engage in other types of dhikr, such as reciting the Qur’an, the enduring good deeds (Al-Baqiyat Al-Salihat), morning and evening adhkar, and comprehensive supplications (du’as) for the good of this world and the hereafter, as these are sufficient. Forgetting them and then remembering them does not indicate an answered prayer or their goodness.