Are there documented reports about Jews around the time of Jesus? And what did they say about the first christians?

Josephus, a Jewish scholar, and historian wrote Antiquities of the Jews, around 93–94 AD. In book 18 Chapter 3 verse 3(Jesus Christ) says:

Now there was about this time Jesus, a wise man, if it be lawful to call him a man; for he was a doer of wonderful works, a teacher of such men as receive the truth with pleasure. He drew over to him both many of the Jews and many of the Gentiles. He was [the] Christ. And when Pilate, at the suggestion of the principal men amongst us, had condemned him to the cross, (9) those that loved him at the first did not forsake him; for he appeared to them alive again the third day; (10) as the divine prophets had foretold these and ten thousand other wonderful things concerning him. And the tribe of Christians, so named from him, are not extinct at this day.

In Book 18 5:2 (John the Baptist)

Now some of the Jews thought that the destruction of Herod's army came from God, and that very justly, as a punishment of what he did against John, that was called the Baptist: for Herod slew him, who was a good man, and commanded the Jews to exercise virtue, both as to righteousness towards one another, and piety towards God, and so to come to baptism; for that the washing [with water] would be acceptable to him, if they made use of it, not in order to the putting away [or the remission] of some sins [only], but for the purification of the body; supposing still that the soul was thoroughly purified beforehand by righteousness. Now when [many] others came in crowds about him, for they were very greatly moved [or pleased] by hearing his words, Herod, who feared lest the great influence John had over the people might put it into his power and inclination to raise a rebellion, (for they seemed ready to do any thing he should advise,) thought it best, by putting him to death, to prevent any mischief he might cause, and not bring himself into difficulties, by sparing a man who might make him repent of it when it would be too late. Accordingly he was sent a prisoner, out of Herod's suspicious temper, to Macherus, the castle I before mentioned, and was there put to death. Now the Jews had an opinion that the destruction of this army was sent as a punishment upon Herod, and a mark of God's displeasure to him.

And in book 20 9:1 (Jesus Christ)

AND now Caesar, upon hearing the death of Festus, sent Albinus into Judea, as procurator. But the king deprived Joseph of the high priesthood, and bestowed the succession to that dignity on the son of Ananus, who was also himself called Ananus. Now the report goes that this eldest Ananus proved a most fortunate man; for he had five sons who had all performed the office of a high priest to God, and who had himself enjoyed that dignity a long time formerly, which had never happened to any other of our high priests. But this younger Ananus, who, as we have told you already, took the high priesthood, was a bold man in his temper, and very insolent; he was also of the sect of the Sadducees, (23) who are very rigid in judging offenders, above all the rest of the Jews, as we have already observed; when, therefore, Ananus was of this disposition, he thought he had now a proper opportunity [to exercise his authority]. Festus was now dead, and Albinus was but upon the road; so he assembled the sanhedrim of judges, and brought before them the brother of Jesus, who was called Christ, whose name was James, and some others, [or, some of his companions]; and when he had formed an accusation against them as breakers of the law, he delivered them to be stoned: but as for those who seemed the most equitable of the citizens, and such as were the most uneasy at the breach of the laws, they disliked what was done; they also sent to the king [Agrippa], desiring him to send to Ananus that he should act so no more, for that what he had already done was not to be justified; nay, some of them went also to meet Albinus, as he was upon his journey from Alexandria, and informed him that it was not lawful for Ananus to assemble a sanhedrim without his consent. (24) Whereupon Albinus complied with what they said, and wrote in anger to Ananus, and threatened that he would bring him to punishment for what he had done; on which king Agrippa took the high priesthood from him, when he had ruled but three months, and made Jesus, the son of Damneus, high priest.

Tacitus a Roman historian wrote Annals in 116 AD in book 15 wrote (Jesus Christ)

Such indeed were the precautions of human wisdom. The next thing was to seek means of propitiating the gods, and recourse was had to the Sibylline books, by the direction of which prayers were offered to Vulcanus, Ceres, and Proserpina. Juno, too, was entreated by the matrons, first, in the Capitol, then on the nearest part of the coast, whence water was procured to sprinkle the fane and image of the goddess. And there were sacred banquets and nightly vigils celebrated by married women. But all human efforts, all the lavish gifts of the emperor, and the propitiations of the gods, did not banish the sinister belief that the conflagration was the result of an order. Consequently, to get rid of the report, Nero fastened the guilt and inflicted the most exquisite tortures on a class hated for their abominations, called Christians by the populace. Christus, from whom the name had its origin, suffered the extreme penalty during the reign of Tiberius at the hands of one of our procurators, Pontius Pilatus, and a most mischievous superstition, thus checked for the moment, again broke out not only in Judaea, the first source of the evil, but even in Rome, where all things hideous and shameful from every part of the world find their centre and become popular. Accordingly, an arrest was first made of all who pleaded guilty; then, upon their information, an immense multitude was convicted, not so much of the crime of firing the city, as of hatred against mankind. Mockery of every sort was added to their deaths. Covered with the skins of beasts, they were torn by dogs and perished, or were nailed to crosses, or were doomed to the flames and burnt, to serve as a nightly illumination, when daylight had expired.

Mara Bar-Serapion a philosopher in ~70 AD wrote to his son (Jesus Christ):

What are we to say, when the wise are dragged by force by the hands of tyrants, and their wisdom is deprived of its freedom by slander, and they are plundered for their superior intelligence, without the opportunity of making a defence? They are not wholly to be pitied. For what benefit did the Athenians obtain by putting Socrates to death, seeing that they received as retribution for it famine and pestilence? Or the people of Samos by the burning of Pythagoras, seeing that in one hour the. whole of their country was covered with sand? Or the Jews by the murder of their Wise King, seeing that from that very time their kingdom was driven away from them? For with justice did God grant a recompense to the wisdom of all three of them. For the Athenians died by famine; and the people of Samos were covered by the sea without remedy; and the Jews, brought to desolation and expelled from their kingdom, are driven away into Every land. Nay, Socrates did "not" die, because of Plato; nor yet Pythagoras, because of the statue of Hera; nor yet the Wise King, because of the new laws which he enacted.

Phlegon, a historian, wrote Contra Celsus Origen in about 140 AD. In book 2 chapter 14, 33, and 59 writes (Jesus Christ)

Celsus, however, accepting or granting that Jesus foreknew what would befall Him, might think to make light of the admission, as he did in the case of the miracles, when he alleged that they were wrought by means of sorcery; for he might say that many persons by means of divination, either by auspices, or auguries, or sacrifices, or nativities, have come to the knowledge of what was to happen. But this concession he would not make, as being too great a one; and although he somehow granted that Jesus worked miracles, he thought to weaken the force of this by the charge of sorcery. Now Phlegon, in the thirteenth or fourteenth book, I think, of his Chronicles, not only ascribed to Jesus a knowledge of future events (although falling into confusion about some things which refer to Peter, as if they referred to Jesus), but also testified that the result corresponded to His predictions. So that he also, by these very admissions regarding foreknowledge, as if against his will, expressed his opinion that the doctrines taught by the fathers of our system were not devoid of divine power.

But, continues Celsus, what great deeds did Jesus perform as being a God? Did he put his enemies to shame, or bring to a ridiculous conclusion what was designed against him? Now to this question, although we are able to show the striking and miraculous character of the events which befell Him, yet from what other source can we furnish an answer than from the Gospel narratives, which state that there was an earthquake, and that the rocks were split asunder, and the tombs opened, and the veil of the temple rent in two from top to bottom, and that darkness prevailed in the day-time, the sun failing to give light? But if Celsus believe the Gospel accounts when he thinks that he can find in them matter of charge against the Christians, and refuse to believe them when they establish the divinity of Jesus, our answer to him is: Sir, either disbelieve all the Gospel narratives, and then no longer imagine that you can found charges upon them; or, in yielding your belief to their statements, look in admiration on the Logos of God, who became incarnate, and who desired to confer benefits upon the whole human race. And this feature evinces the nobility of the work of Jesus, that, down to the present time, those whom God wills are healed by His name. And with regard to the eclipse in the time of Tiberius Cæsar, in whose reign Jesus appears to have been crucified, and the great earthquakes which then took place, Phlegon too, I think, has written in the thirteenth or fourteenth book of his Chronicles.

He imagines also that both the earthquake and the darkness were an invention; but regarding these, we have in the preceding pages, made our defence, according to our ability, adducing the testimony of Phlegon, who relates that these events took place at the time when our Saviour suffered. And he goes on to say, that Jesus, while alive, was of no assistance to himself, but that he arose after death, and exhibited the marks of his punishment, and showed how his hands had been pierced by nails. We ask him what he means by the expression, was of no assistance to himself? For if he means it to refer to want of virtue, we reply that He was of very great assistance. For He neither uttered nor committed anything that was improper, but was truly led as a sheep to the slaughter, and was dumb as a lamb before the shearer; and the Gospel testifies that He opened not His mouth. But if Celsus applies the expression to things indifferent and corporeal, (meaning that in such Jesus could render no help to Himself,) we say that we have proved from the Gospels that He went voluntarily to encounter His sufferings. Speaking next of the statements in the Gospels, that after His resurrection He showed the marks of His punishment, and how His hands had been pierced, he asks, Who beheld this? And discrediting the narrative of Mary Magdalene, who is related to have seen Him, he replies, A half-frantic woman, as you state. And because she is not the only one who is recorded to have seen the Saviour after His resurrection, but others also are mentioned, this Jew of Celsus calumniates these statements also in adding, And some one else of those engaged in the same system of deception!