The parallel passages are found in Mark 15:16-32, Luke 23:26-43, and John 19:17-24.
The crown of thorns was actually acanthus, a flowering bush with prickly leaves. We can’t tell if the purple robe was the one Antipas had put on Him or something kept in the fortress for Roman use. The Roman soldiers on duty in this fortress were mostly conscripts from Syria. The mutual contempt between Syrians and Jews is well known historically. We can’t tell if Matthew and Mark refer to a second round of the soldiers mocking Jesus, but they eventually place Him in custody of a squad of four appointed to escort every condemned man. The cross beam was already prepared, but Jesus was unable to carry it very far.
A man named Simon was coming into town from the opposite direction. He was a Diaspora Jew from Cyrene, a major city with a large Jewish community, now in ruins standing on the shore in modern Libya, toward the eastern end of the coastline. It’s quite likely Simon was chosen in part because he was a large fellow, but also because he was the only one coming against the flow of traffic surrounding this procession. Mark notes that this man had two sons known to his audience, where he composed his Gospel in Rome: Alexander and Rufus. At any rate, this Simon was forced to carry the crossbeam, since Jesus was half dead already.
I suppose this is as good of a place as any to note that there is no Gospel record that Jesus fell at any time on the route. There’s a lot of pious nonsense about this scene. The Gospels don’t linger much over the details. We have no conclusive evidence indicating where Golgotha stood, except that it was outside the city limits of that time. The place for crucifixion would offer permanently fixed upright posts or even a framework atop a high spot that would be prominently visible as a warning to others. There would have been skeletal remains scattered around, since victims with no one to claim the body were left there until the carrion eaters consumed their flesh.
Luke does record that Jesus had a word for the weeping women from His entourage of disciples who lived in Jerusalem. Keep in mind that Jesus had already gotten past His sorrow in the garden, so He encouraged the women to save the weeping for their own coming trials. He reminds them of the coming destruction of the city. If the Jewish leaders could be so hateful and barbaric under God’s patience, how will they treat the people when divine wrath comes on them?
The victims of crucifixion were offered a painkilling mixture. It was composed of the cheap wine supplied to the soldiers in their rations. It would have been the latter end of a batch coming out of the grape vat, with the dregs and not much sugar. When fermented it was more like vinegar than wine. Mixed into this was myrrh, which had an analgesic effect. Jesus refused His drink. There were two other actual criminals sentenced to die on the same day. Jesus was placed in the middle between them, fulfilling the prophecy in Isaiah 53:12.
During the process, Jesus prayed out loud that His Father would forgive the soldiers, since they had no idea who He really was. Having to guard these convicts until they were dead was a dreary duty for the soldiers, but they were permitted to plunder their victims, since crucifixion required they be naked. John notes they decided to cast lots for His seamless outer robe, instead of dividing the fabric among themselves. This fulfilled another prophecy (Psalms 22:18).
There was a bit of fuss over the charge mounted above Jesus’ head; the Sanhedrin weren’t happy. Pilate had mocked them by writing that Jesus /was/ the King of the Jews, not merely that He had claimed to be. For this, the accompanying soldiers mocked Jesus. The Jewish leadership witnessing His death recounted some of His parabolic statements, twisting them to have a literal meaning. One of the criminals hanging beside Jesus, despite his own misery, joined in this mockery, but the other insisted Jesus was an innocent man. Luke notes the latter asked Jesus for eternal mercy, and Jesus promised they would be in Heaven that same day.
It cost the men a bit of effort to speak at all. We have very few historical details and a mass of mythology obscuring the process of crucifixion. Our best guess is that the men were hung in such a way as to lean far forward, nearly choking from the position of their arms and shoulders above and behind them. Their feet were affixed, most likely nailed from the side through the heel bones, with their knees bent somewhat. They could push up with their legs against the pain of the spikes to catch their breath, but eventually slumped back down with exhaustion, only to nearly asphyxiate again. There’s no reason to assume they were positioned very high off the ground.
The Romans had developed an exceptionally torturous form of death that took hours, even days if the victims were particularly hardy.