The centering of the screen is extremely irritating, each move moving somewhere to the center of the map.
I've noticed this too. I'll see if it's something I can correct, but it might be a side effect of some events which can't be entirely prevented.
Barbarians are pouring in bundles, but they cannot kill anyone.
I'm not sure how many turns you've played, but there are some stronger barbarians coming later. (For example, Vikings can be pretty tough if you don't have City Walls.)
An archer is stronger than a catapult.
No, but a catapult is an artillery unit and all artillery are capped at doing 50% damage to an enemy. It's your choice to play without reading the documentation

but this is explained there!
An incomprehensible unit, the Visigoth militia, appears and disappears.
It turns out that when events change terrain
improvements (roads, irrigation, etc.) on tiles you've already explored, your view of the map doesn't update to show you the changes. This can be really confusing since a terrain that
looks irrigated isn't necessarily
producing extra Health like you'd expect. To fix this, I have the events create one of your units on the affected tile and immediately delete it again; this updates your map view so it is always correct. On my PC, the unit is created/deleted so quickly that I can't even see it; sorry if it's more visible to you, but I still think it's better than the alternative of a misleading map.
My nation is the most backward (6th or 7th place in F8). I play at maximum difficulty, with maximum barbarians. However, I don't remember ever having to be an outsider with an AI.
Yikes!

I can't come
close to beating this on max difficulty and max barbarians, and I know all the tricks!
I'd recommend that most players use "Duke" or easier difficulty for their first game, but hey, do what's fun for you!
I use the "full immersion" method in the game. I did not specifically read any explanatory files, but try to act at random - as happened in real history (and also, as I played more than 20 years ago, when I met civ2).
Again... not what I'd recommend, but if that's your favorite way to learn how the scenario works, go for it!