The laying on of hands in the Old Testament was a way of passing on blessings and authority. It was also used to set apart people and animals for service to God, or to render judgment. The Apostles kept this practice. Practically every instruction for sacrifoce in Levitocus involves the laying on of hands, so I won’t quote all of those, but here are some other examples:
Gen 48: 14 And Israel stretched out his right hand and laid it upon the head of E′phraim, who was the younger, and his left hand upon the head of Manas′seh, crossing his hands, for Manas′seh was the first-born. 15 And he blessed Joseph, and said . . .
Num 8: 10 When you present the Levites before the Lord, the people of Israel shall lay their hands upon the Levites, 11 and Aaron shall offer the Levites before the Lord as a wave offering from the people of Israel, that it may be theirs to do the service of the Lord.
Deut 34: 9 And Joshua the son of Nun was full of the spirit of wisdom, for Moses had laid his hands upon him; so the people of Israel obeyed him, and did as the Lord had commanded Moses.
You see it in the New Testament for confirmation, the annointing of the sick, and ordination, at the least. The letters to Timothy instruct on ordination. It’s also a clear practice of the early Church from its earliest days.
Keep in mind that none of the New Testament writings are a priestly manual like Leviticus was, so much of the practices of the first elders and presbyters were passed down through tradition. Still, 1 and 2 Timothy does clearly speak about ordination and how it involved the laying on of hands.
Regarding acting in the person of Christ, there is…
2 Corinthians 2: 10 Whomever you forgive anything, so do I. For indeed what I have forgiven, if I have forgiven anything, has been for you in the presence of Christ …
The Greek literally speaks of Paul putting on the “face” of Christ, like an ancient Greek actor putting on a mask and acting as another person. It is literally "in the face of Christ; it is sometimes translated as “in the person of Christ,” that Paul forgives the offendor.