What were Jesus and early Christians like?

[TimOneill]

So on the issue of Q, I was reading about the Farrer hypothesis that claims:
Mark -> Matthew
Mark + Matthew -> Luke
https://en.wikipedia.org/wiki/Farrer_hypothesis
As I was looking at the similarity in content and sequence of the hypothesized Q material in Matthew and Luke, it is hard to believe that these gospels were independently taking quotes from Q. It seems much easier to believe that Luke used Matthew.

Similarity of sequence? There is no such similarity. On the contrary, the differences in where gMatt and gLuke place the common Q material in their common Marcan framework is one indication that they are working independently with the same material.

Why do scholars assume that Luke did not use Matthew? Did they assume that differences in the nativity stories implied independence? Why not assume that Luke was "correcting" Matthew to match the views of a particular Christian faction?

It’s a conclusion, not an “assumption”. This article summarises the reasons most scholars accept that gLuke and gMatt used the Q material independently and why they don’t accept that gLuke depended on gMark and gMatt instead. Note in particular the section headed “Matthew’s and Luke’s Handling of the Double Tradition”, which gives the three main reasons it is agreed that gLuke did not use gMatt.

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What I want to know is who wrote the damn things.

I’d like to know that about many anonymous ancient sources. I’d also like more sources, closer sources to the events in question and sources with better indications of where the ancient authors got their information (footnotes would be nice as well). Unfortunately, I’m unlikely to get any of these things. Welcome to the study of ancient history.

Being in the third person, it appears to be someone either making it all up, or following some dude around and writing about him. It seems very unlikely to me it would be the named guy writing it.

What “named guy”? None of the gospels name their writers – those are later editorial additions.

Or maybe just hearsay about people who may or may not have existed.

Most ancient sources are what you keep calling “hearsay”. That’s just the nature of the material we have. And “may not have existed” is not the default position. “Probably existed, though we can’t be certain” is.