Lord, Lord, did we not in Your name perform many miracles? Who were these?

[TonyChanYT]

NIV, Mark 9:

38 “Teacher,” said John, “we saw someone driving out demons in your name and we told him to stop, because he was not one of us.” 39 “Do not stop him,” Jesus said. “For no one who does a miracle in my name can in the next moment say anything bad about me, 40 for whoever is not against us is for us. 41 Truly I tell you, anyone who gives you a cup of water in my name because you belong to the Messiah will certainly not lose their reward.

Jesus will reward this person for using his name to perform a miracle even though John did not recognize him as a follower. But then, Matthew 7:

22 Many will say to Me on that day, ‘Lord, Lord, did we not prophesy in Your name, and in Your name cast out demons, and in Your name perform many miracles?’ 23 And then I will declare to them, ‘I never knew you; leave Me, you who practice lawlessness.’

They knew about Jesus and the verbal methods but Jesus never G1097-knew them intimately. The knowledge was one-sided. It was not a bi-directional relationship.

What was the power source behind the miracles, signs, and wonders?

It could come from Satan, 2 Corinthians 11:

14 no wonder, for Satan himself masquerades as an angel of light.

However, ultimately, all powers came from God, Psalm 62:

11 One thing God has spoken, two things I have heard: “Power belongs to you, God,

Was the Matt passage talking about genuine signs and wonders of God or counterfeit miracles of Satan?

It could be either.

Can God actively use someone in signs and wonders and still prohibit them from entering His kingdom?

Yes, the person can fall away from God later in his life, 2 Peter 2:

20 If they have escaped the corruption of the world by knowing [G1922] our Lord and Savior Jesus Christ and are again entangled in it and are overcome, they are worse off at the end than they were at the beginning. 21 It would have been better for them not to have known [G1921] the way of righteousness, than to have known [G1921] it and then to turn their backs on the sacred command that was passed on to them.”

Strong's Greek: 1921. ἐπιγινώσκω (epiginóskó) — 44 Occurrences

BDAG:
① to have knowledge of someth. or someone, know

They have a G1922-knowledge of the Lord, and they G1921-know the way of righteousness, but Jesus does not G1097-know them intimately. These people know Jesus on paper but not the living Jesus in their hearts. They know the Word of God on paper but not the living Word. They do not have a daily living relationship with Jesus. They are 1-directional Christians. They G1921-acknowledge Jesus with their lips, but Jesus does not G1097-know them. Performing miracles in Jesus' name is no guarantee to eternal life; only an intimate bi-directional relationship guarantees that.

Paul explained in Philippians 1:

18 What then? notwithstanding, every way, whether in pretense, or in truth, Christ is preached; and I therein do rejoice, yea, and will rejoice.

Even 1-directional Christians can perform miracles and preach the true Christ.