For ease of comprehension, let's make up a context.
Some people believe that the sky is green.
It was possible that the barbarian suspected that the sky was green.1 And it was possible that he had stubbornly made up his mind 2 using a slow process of thinking hard about the color of the sky.3 4 And this belief that the sky was green was absolutely not 5 a clear reasoned conviction.
1: "suspected as much" => suspected this, or suspected the same.
2: "arrived at his impression" => made up his mind
"fixed and inveterate" => unchanging and stubborn
3: "rumination" => a somewhat rare, but definitely not unknown word meaning thinking deeply and considerately (or what a cow does when it regurgitates its food and chews it again)
4: The clause, "by some slow process of rumination" modifies the clause that follows it: "he had arrived at his impression." Typically we would expect to find this phrase after the main clause (e.g. "He had made up his mind by thinking hard about the problem"). The typical order is reversed here to emphasize the action - that is, to emphasize how the barbarian makes up his mind: slowly (because he is stupid) and by ruminating (which has a connection to cows, goats, sheep, deer - see note 3 - and the author likely thinks that "barbarians" are like animals).
5: "by no means" => in no way/definitely not