quickening means to bring to life And you hath he quickened, who were dead in trespasses and sins; Ephesians 2:1By quickening spirit - a term I've never heard used - I would suppose that you mean that Jesus makes us alive.
yes the holy spirit was in the o.t He came up on people in today he dwell in us LOOK AT SAMSON JUDGES 16 HIS strength came from the Lord who gave it through the spirit .through Samson's obedience he was told not to cut his hair..In the OT Jesus had not yet appeared as Savior - was He still a quickening spirit?
I ask because persons knew the Holy Spirit even in the OT but He did not dwell with them as in the NT.
judges 16
17 That he told her all his heart, and said unto her, There hath not come a razor upon mine head; for I have been a Nazarite unto God from my mother's womb: if I be shaven, then my strength will go from me, and I shall become weak, and be like any other man.
18 And when Delilah saw that he had told her all his heart, she sent and called for the lords of the Philistines, saying, Come up this once, for he hath shewed me all his heart. Then the lords of the Philistines came up unto her, and brought money in their hand.
19 And she made him sleep upon her knees; and she called for a man, and she caused him to shave off the seven locks of his head; and she began to afflict him, and his strength went from him.
20 And she said, The Philistines be upon thee, Samson. And he awoke out of his sleep, and said, I will go out as at other times before, and shake myself. And he wist not that the Lord was departed from him.
Genesis 6:3
“And the LORD said, My spirit shall not always strive with man, for that he also is flesh: yet his days shall be an hundred and twenty years.”