Who was the naked boy in the woods with Jesus and the apostles in Mark 14:51-52, and what was he doing there?

They were being arrested. What makes you think they were in the woods?

John 18:15 mentions a disciple known to the high priest. Is this the same disciple who earlier fled “naked,” as reported at Mark 14:51, 52?

No, it seems that the person known to the high priest was the apostle John, whereas it was the disciple Mark who fled “naked.”

Taking these accounts in time sequence, we start at the garden of Gethsemane. The apostles reacted in fear when Jesus Christ was arrested. “They all abandoned him and fled.” The very next verse in Mark’s account draws a contrast: “But a certain young man wearing a fine linen garment over his naked body began to follow him nearby; and they tried to seize him, but he left his linen garment behind and got away naked.”

Thus, the initial response of the 11 apostles is contrasted with that of this unnamed disciple, so it is logical to conclude that he was not one of the apostles. This incident is recorded only in the Gospel written by the early disciple John Mark, the cousin of Barnabas. Hence, there is reason to hold that Mark was the “certain young man” who began to follow the arrested Jesus but who fled without his covering garment when the mob tried to apprehend him too.

The "naked boy" from this text is Mark himself.

It all started in the garden of Gethsemane when Jesus' disciples fled from him because he was arrested and feared that they would also be arrested.

Their is a contrast between the 11 disciples of Jesus and this one that was actually following Jesus instead of running away meaning that this "boy" following Jesus was not one of these disciples. This naked boy is only mentioned in the gospel of Mark, also making it clear that it was Mark. John Mark cousin of Bernabe. His cloth probably fell when he was almost caught by the guards but fled.

In the garden of Eden Adam and Eve were naked and ashamed, in the garden of Gethsemane with Christ's obedience the shame would be removed. We can now be clothed with the righteousness of the Christ. This is how I interpret this unusually placed verse. A foreshadowing.

Traditionally believed to be John Mark, one of the youngest of the Apostles, but nobody knows for sure, as it is not stated.

That was most likely Mark, himself. The structure of the sentence indicates it is a modest self-reference. If this is true, it is the only existing eyewitness account of the life of Jesus.

They were sleeping.

It's not Jesus' fault! It's those guys he hangs out with. Where are you gonna find 12 straight upholsterers?

It is a metaphor.Ask Him.