What facts about Jesus do we have, from a scientific point of view?
I think 3 authors mention him: Flavius Josephus, Tacitus and the 3rd I forgot.
What did Jesus really say and what is only attributed to him?
To try and keep this short, we have more evidence for the person Jesus of Nazareth than any other major figures in all antiquity.
Very rarely will you have 4 biographies of the same person, as well as many references of him in these early letters from Paul, references from Roman extra-biblical literature, and Jewish references to Jesus. The idea that Jesus of Nazareth never existed is an idea that no serious historian entertains. It's by these left wing fringe elements of Jesus mythicism that they propagate these baseless accusations, really no scholar takes seriously. If you don't believe me, take
it from a NT scholar Bart D. Ehrman who is a non-Christian, and from Richard Dawkins, a known atheist.
However, the NT shows so many things that cannot possibly be scientifically explained due to the nature of them, i.e. Jesus' miracles and His death and resurrection. There is good evidence for the resurrection if one is to seriously seek, but ultimately, it comes down to faith as being a Christian. We see this in the case of Thomas who wouldn't believe unless he could touch the nail prints in Jesus' hands and thrust his hands into his side. (John 20:27-29)
Then he said to Thomas, “Put your finger here; see my hands. Reach out your hand and put it into my side. Stop doubting and believe.” Thomas said to him, “My Lord and my God!” Then Jesus told him, “Because you have seen me, you have believed; blessed are those who have not seen and yet have believed.”
It is good to know your faith inside and out, but Jesus does place high regard for a person who didn't need proof to believe in Him but only through faith. And Jesus commends them as truly blessed.
What did Jesus really say and what is only attributed to him?
Your third question is based on whether the NT documents had been altered during the 2000 years from the original. The answer is quite simply no. The Bible we have today is essentially exactly what was read by the early church Christians. We have writings of antiquity which were copied and recopied across the centuries, right up to the time of the invention of the printing press in the west in the 15th century.
There is a science called Textual Criticism which examines the documents to see whether they have been altered through the copying and the recopying, and which corrects the documents on the basis of better texts. This is a highly technical field, and the results of it are what interest us, not the means of what those results contained, but the results of textual criticism applied to the NT documents is very simple. The NT documents are the best attested documents of the ancient world. That is to say that there is the least difficulty going back to the original content of those documents compared to any of the documents of antiquity.
There is the least textual alterations and damage compared to other documents of antiquity. In general the distance between the first complete texts we have of a classical writer and the original writing, ranges from 900-1,000 years. We don't know what happened in that period, and we simply assume that the document we have simply represents the documents as it was originally written.
Whereas in the case of the NT, there are documents that is to say - fragments, lectionary readings, quotations in the like that carry us from the complete text that are immensely closer to the original writings show no alterations.
The NT we have today is essentially what was read by the early church Christians, and it is by faith on whether to believe it was said by Jesus or not.