Is it true that sometimes when I am driving, walking, sitting, or reading, I remember Allah with supplications such as "O Living, O Self-Subsisting, by Your mercy I seek aid," or "O Allah, I ask You for pardon and well-being," or "Our Lord, grant us good in this world and good in the Hereafter, and save us from the torment of the Fire," without starting with praise to Allah and prayers upon His Messenger, because I heard that supplication remains suspended without praying upon the Prophet, peace and blessings be upon him?

Supplication is the essence of worship. There are supplications narrated from the Prophet, peace and blessings be upon him, including: "O Living, O Sustaining, by Your mercy I seek assistance" when in distress, and "O Allah, I ask You for well-being in this world and the Hereafter," and "O Allah, our Lord, grant us good in this world and good in the Hereafter, and protect us from the punishment of the Fire." It is desirable to begin the supplication by mentioning Allah and sending blessings upon the Prophet, but this is not a condition. So, if someone forgets or does not recall the etiquettes of supplication, there is no blame upon him, because error and forgetfulness are lifted from this Ummah.