Does Allah's name "Al-Qayyum" mean Self-Subsisting, and does it come from the word "qā'im" which means "existing"? And if not, is there a name of Allah that means "existing"? And is the word "mawjud" (existing) Arabic, and if so, why was it not mentioned in the Holy Quran while the word "wajada" (found/existed) was mentioned?

Al-Qayyum is one of the Most Beautiful Names of Allah, and it carries the meaning of Allah's existence, just as all of His names carry this meaning. Al-Qayyum is the One who exists by Himself, and by whom the heavens, the earth, and everything in them subsist. He is the Ever-Existing, the One who manages the affairs of creation, the All-Knowing of all matters. Al-Qayyum means the One who subsists by Himself and sustains others, and this can only be attributed to Allah Almighty. Allah's Name "Al-Qayyum" indicates His eternality (without beginning), His everlastingness (without end), and His being the Necessarily Existent. Allah truly exists, and His existence is known by necessity; it is an attribute of His, and it is permissible to describe Him with it.