What is the ruling on saying "Our Master Muhammad," and does it conflict with the sovereignty of Allah? And does saying "My Lord, forgive me" differ from "O Allah, I ask You for forgiveness" in terms of the imperative form?

There is no impediment to uttering the word "sayyiduna" (our master) or "sayyidi" (my master) before mentioning the Prophet, peace and blessings be upon him; for he is the master of the first and the last, and the master of the children of Adam. However, it is not permissible to use the definite article "al-" (the) with "Sayyid" (i.e., "al-Sayyid" - The Master) except for Allah Almighty, because absolute sovereignty belongs to Allah alone.

There is no difference between saying: "Lord, forgive me" or "O Allah, I ask You for forgiveness." Both are supplications (du'a) to seek forgiveness from Allah Almighty, for a request from a lower to a higher being is called a supplication.