What is the ruling of Islamic law on one who believes that being occupied with dhikr, reciting Surat Al-Ikhlas, and sending blessings upon the Prophet (peace and blessings be upon him) at home is better than regularly performing the prescribed prayers, thinking that by doing so he obtains the reward of prayer and its benefits, such as raising one's status and expiating sins?

Your understanding that acts other than prayer, such as remembrance (dhikr) and awaiting prayer, can compensate for the reward of prayer and take its place is incorrect. Prayer is the best voluntary physical act of worship after the two declarations of faith, either absolutely or after jihad and seeking knowledge, depending on the scholarly difference of opinion. Prayer combines many acts of worship, such as remembrance, recitation, and sending blessings upon the Prophet. That is why it was the delight of the Prophet’s eyes (peace and blessings be upon him) and superior to other voluntary acts. Furthermore, recitation, remembrance, and sending blessings upon the Prophet (peace and blessings be upon him) performed within prayer are better and yield a more complete reward than when performed outside of it. Therefore, increase your prayers, for performing voluntary prayers is the best voluntary act and the greatest means of drawing near to Allah.