lilly....What you posted were historical records of early Christianity as it was in the early second century (in the case of Tacitus, Pliny, and Lucian), or the later second or third centuries (in the case of rabbinical references), and they are valuable and informative on early Christian practice, Roman attitudes towards Christians, and so forth. When when something like Pliny's description of Christian worship is then pressed into becoming "independent evidence" of the historical Jesus, that is taking things too far. Pliny mentions Christ only as the object of Christian adoration and worship in his own day; he provides nothing of historical value pertaining to the life of Jesus of Nazareth, no more than a description of the activities of Buddhists would furnish information on the historical Siddhartha. Whatever he says about his observations of Christians as he saw them is clearly drawn from his own personal interactions with them, so he hardly supplies "independent" testimony of Jesus from a separate non-Christian source. Pliny simply describes what he sees the Christians doing.
The same goes with the notices of Tacitus and Lucian...these are similarly dependent on Christian reports. The reference in Tacitus is far more important than the one in Pliny because he does at least make explicit reference to the author of the religion and he mentions him as a person who lived and died at a particular place and time. But as I mentioned in my last post, his notice shows the signs of hearsay dependence on Christian kerygma about Christ (e.g. "Christ" is what Christians called their founder and not what independent Roman sources would have called him, the incorrect title of "procurator" is what people in his day would have called the office of governor and not what actual Roman records of Pilate would have said, and the content of the statement is found in early credal formulations like those in Ignatius, Magnesians 11:1, Trallians 9:1, Smyrnaeans 1:2; Justin Martyr, Apology 1.13.3, 1.61.13, Irenaeus, Adversus Haereses 2.23.4, 3.4.2, etc.), and it is unlikely that he would have undertaken archival research on what he regarded as a "pernicious superstition", especially one with so recent vintage.... he would have been happy to accept what Christians were saying at face value because it only further supports his negative depiction of Christians (in Roman thought, the greater the antiquity of a religious tradition, the more respectable it is). Moreover, Tacitus was proconsul of Asia around the same time Pliny was governor of Bithynia (i.e. in AD 112-113, and he wrote Annals in c. AD 117), and in fact he was a personal friend of Pliny, who not only wrote about Christians but who also interrogated them personally and thus probably heard their creed when they testified their faith in the face of persecution. It is therefore far more probable that he had firsthand or secondhand knowledge of the "superstitution" and its creed than the alternative.
Christ being crucified under Pontius Pilates reign would have been public knowledge.
It would have been public knowledge precisely because of Christian preaching and evangelism. That is where the average person would have heard that Christ was "crucified under Pontius Pilate"; this was a very basic element of the Christian faith that was being spread far and wide by missionaries, evangelists, and ordinary Christians who wanted to share their faith. But back in AD 33 or whenever it was, the actual crucifixion of Jesus would hardly have been something the average Roman citizen would have even heard about. From the Roman point of view, it was just one out of countless other executions of slaves, troublemakers, thieves, etc. taking place all throughout the empire, much less in a backwater province like Judea. Jesus would have only spent a very brief amount of time before Pilate (just a few hours in a single day), who executed him among several other people slated for execution, at the busiest time of the year in Jerusalem -- who knows how many other seditious people there were (like Barabbas, who also would have been slated for execution) that would have shared the same honor as Jesus during the Passover season, let alone the rest of the year, let alone throughout Pilate's tenure as prefect (indeed, Josephus suggests that Pilate had to frequently deal with this problem). Yet by the turn of the century, there were thousands of Christians throughout the empire trumpeting the fact that Jesus had been crucified under Pontius Pilate, as a fundamental article of faith. While Jesus was a complete nobody to the average Roman during the time he lived, he was everything to his small band of followers who in the decades since expanded into a sizeable movement. If the assertion that he was crucified under Pontius Pilate was publically known in the second century, it was through their efforts to make that publically known.
Note that I am not assessing the validity of the information provided by either Tacitus or Christian sources like the gospels or Ignatius. What I am assessing instead is the likelihood that Tacitus furnishes independent testimony about the life of Jesus, i.e. independent from Christian testimony or influence.