Q. Are Satan and the anti-Christ the same person?
Also, If God, Jesus and the Holy Spirit are the same person why do we say and I will sit at the right hand of God the father? How can that be?
A. Satan and the anti-Christ are not the same person, but at the beginning of the Great Tribulation Satan will indwell (possess) the anti-Christ becoming the source of his power. (Rev. 13:4) Then in Rev. 19:19-20 we read that the anti-Christ and false prophet are captured and thrown into the Lake of Fire, while in Rev. 20:1-3 Satan is captured and confined for 1000 years. This shows that they are two different personages.
No one fully understands the nature of the Triune God. They can be seen as three, but are also one. The notion of Jesus sitting at the right hand of the Father comes from Psalm 110 where He is told to sit there while the Father subdues all His enemies. At that time all authority would be given to the Son, (Matt. 28:18) until the last enemy, death, is defeated. (1 Cor 15:24-28)
Your quote could also refer to the fact that when Jesus became a man, it was a permanent transition. In other words He’s still a man and always will be. In that sense he is permanently a separate physical entity in which the Father dwells. (Col. 1:19) I know it sounds confusing, but it’s one of those things the Bible asserts but never explains.