The First Circle is a deep exploration of so many things. Friendship, Stalinism, Marx, Marxist Dialectic, Christianity, Catholicism, Jews, and so on. No one comes out of it clean and Solzhenitsyn doesn't think he has the answers. Two things the book is sure of are: suffering is real and being does not determine consciousness (contrary to Marx's dictum).
I believe the attempt to frame Solzhenitsyn as a reactionary and antisemite is wrong. It stems from him saying things you're not supposed to say about Jews being overrepresented in the early Soviet prison system (an empirical question) and failing to condemn Putin as much as the West would like. Solzhenitsyn was highly critical of Gorbachev for seeming to put his reputation with the West ahead of his country. It's clear Solzhenitsyn wanted to avoid that.
Also, regarding his alleged antisemitism, The First Circle contains a narrative about Stalin turning against the Jews highly placed in the Soviet prison system. Solzhenitsyn's view here is nuanced. I haven't read 200 Years Together but I highly doubt it's slavering antisemitism. And 99% of the people claiming it is haven't read it either.
This is where he got his history lessons: https://en.wikipedia.org/wiki/Andrey_Dikiy
I highly doubt Solzhenitsyn was an antisemite based on what I've read of him (there are plenty of Jewish characters). I could be wrong (I haven't read everything) but I strongly suspect that this is one more example of unhinged culture warriors connecting dots based on their preconceived ideas of what is and isn't acceptable to say and think.
No, it's a neologism that intentionally points out that there is a bias towards moderation that assumes that the more central a position is, the more right it is. People prone to this bias are more easily manipulated by changing the framing of a question, and trust people more who scrupulously avoid consistent positions.
e.g. If Jewish Russians are trying to conquer and run Russia for their own pleasure and to avoid work at the expense of non-Jewish Russian death and suffering, attacking them is self-defense. However, if attacking Jews is wrong, then they can't be trying to take over Russia to oppress non-Jewish Russians. Maybe we should just have a little pogrom, or a special tax.
I highly doubt you've read the book you're criticizing and I grant roughly zero chance that you've fairly summarized Solzhenitsyn's argument ("the Jews kind of had it coming because they tried to rule the Russians" or whatever nonsense). Your framing is exactly what I'd expect from someone with the mind virus infecting the people who use "both-sides" as a verb.