All of these questions about Jesus' claims center around a misunderstanding of the nature of what Christ is and who was The Christ that was mentioned in scripture and also how the word Christ relates to us. To understand what 'Christ' means clears up many misunderstandings about Jesus' claims. (Also, to misunderstand the word 'Christ' does not make one an anti-Christ, which is an accusation that has been made worthless by its frivolous use.)
Mark 7:10 For Moses said, `Honor your father and your mother';...
When Moses gave a command, he would simply tell them what to do, but yet he spoke in the name of the LORD. That doesn't mean he said 'In the Name of the LORD' after every breath, but that to Israel he was the LORD even though a man cannot truly be that. The Scripture says that Moses was faithful in all the LORD's house, which implies that lots and lots of authority had been given to Moses, perhaps even 'All power in heaven & earth' in the sense that Jesus used the phrase. Additionally, Moses left orders that one day there would be a prophet like (equal) to himself. Deuteronomy 18:15 "The LORD your God will raise up for you a prophet like me from among you, from your brethren -- him you shall heed --" John 1:45 Philip found Nathanael, and said to him, "We have found him of whom Moses in the law and also the prophets wrote, Jesus of Nazareth, the son of Joseph."
Finally, the anointing of Christ (the name which is above every name) which is upon Jesus also is upon us as we are filled with the Spirit through Scripture but more through another of God's influences upon us. Jesus continues to work with us from where he is now to get everything accomplished just as planned. He is the chief architect. He is exalted to the highest place at the 'Right hand' of God, which is also called the 'Household of Faith', the 'Bride of Christ', and 'The Church' of which Jesus is the only chief. Even that position he will one day relinquish, in order to undo a terrible error which our 'Household of Faith' once made which was to choose a man to be king instead of choosing God. Even this will be brought to an end through Jesus. I Corinthians 15:24 "Then comes the end, when he delivers the kingdom to God the Father after destroying every rule and every authority and power." and I Samuel 8:7 And the LORD said to Samuel, "Hearken to the voice of the people in all that they say to you; for they have not rejected you, but they have rejected me from being king over them.
Ephesians 3:14-21 For this reason I bow my knees before the Father, from whom every family in heaven and on earth is named, that according to the riches of his glory he may grant you to be strengthened with might through his Spirit in the inner man, and that Christ may dwell in your hearts through faith; that you, being rooted and grounded in love, may have power to comprehend with all the saints what is the breadth and length and height and depth, and to know the love of Christ which surpasses knowledge, that you may be filled with all the fullness of God. Now to him who by the power at work within us is able to do far more abundantly than all that we ask or think, to him be glory in the church and in Christ Jesus to all generations, for ever and ever. Amen.
Ephesians 5:17-21 Therefore do not be foolish, but understand what the will of the Lord is. And do not get drunk with wine, for that is debauchery; but be filled with the Spirit, addressing one another in psalms and hymns and spiritual songs, singing and making melody to the Lord with all your heart, always and for everything giving thanks in the name of our Lord Jesus Christ to God the Father. Be subject to one another out of reverence for Christ.