Jesus uses a question to make the religious leaders think deeply about the Psalm he is about to quote. AT: "Then, tell me why David in the Spirit calls him Lord" (See: [[rc://en/ta/man/translate/figs-rquestion]])
Here "my" refers to God the Father. The "right hand" is often used to indicate a place of honor. When referring to God, since God has no physical body or hands, to sit at God’s “right hand” is an idiom that means that Christ will rule as God, with God’s authority. AT: "here in my place as we rule together as king." (See: rc://en/ta/man/translate/figs-idiom)