Know Thy Talmud #1 (The Talmud Conspiracy)
Know Thy Talmud #3 (What You Need to Know)
If the Talmud is quite evil, surly it must be easy to just link to an online version and cite it talking about how to kill all non-jews, steal from them or enslave them? Actually no, if it was that easy, then everyone on the planet would have already known about the Jewish Talmudic problem, you just can't expect an online Talmud version put up by an ex-google engineer to really put it out on the open now would you?
You can't easily cite the evils in the Talmud for the following reasons:
1-The Talmud is massive, in some prints, well over 20 volumes! And that's just the Babylonian Talmud, there is the Palestinian Talmud (Considered less credible), and there is the mystic version, the Zohar, and there are many, many more books and commentaries or abridged versions. In addition the Talmud (Babylonian), its laws (Mishna) are written in special Hebrew, you can't just study ordinary Hebrew to understand it correctly, the commentary and explanatory parts (Gemara) are written in Aramaic (anyone remember when Israeli ISIS tried to destroy the only city in existence which speaks it (Maaloula, Syria)), The Palestinian Talmud Gemara is written in different form of Aramaic (Western). And I can go on and on, basically it's quite difficult to wade through the Talmud for its size and ancient language, Christian Europe only discovered its evil around the 13th century!! And it happened through the few jewish converts such as (Nicolas Donin, Pablo Christiani, Johannes Pfefferkorn)
Additionally, there has been many disputations, such as the Lwów disputation in September 1759 involving Jacob Frank.
2-Because the Talmud was discovered to be evil on various occasions which led to pogroms and its burnings (France 1242, in addition to Rome and Barcelona); "Clean" or "Expurgated" versions of the Talmud were eventually used while the "original" versions hidden in synagogues. One of the first expurgated versions was one printed in Basil 1578-1581. The versions which contain all the clear references are the Venice version printed in 1520-1523 by Daniel Bomberg, and the Amsterdam version printed in 1644-1648. If you want a hint to know that you are on to something, try buying one of those version or any old Talmud versions for that matter!!!
In short: Due to government and self censorship, all "modern" Talmud versions do not have the exact clear terms, instead they are deleted or renamed with words the Rabbis understand, (Jesus sometimes renamed into "the one whose memory shall be erased" etc..)
If this is the case, then how do we know about its evils? There are still references of those who examined those issues such as: Talmud Unmasked
Additionally there are many books on the subject, unfortunately these books are disappearing by the day! Please do save the info I have written and the PDFs I linked such as the Talmud Unmasked.
As I said in part 1: The entire Talmud is relatively stable online in its three sections (Bavli or Babylonian is the biggest and often mistaken for the whole). Tracking individual medieval rabbinic opinions is indeed difficult but these are rarely authoritative.
https://www.sefaria.org/texts/Mishnah
https://www.sefaria.org/texts/Talmud/Bavli
https://www.sefaria.org/texts/Talmud/Yerushalmi
Part 2 here is not too far off the mark. The biggest problem with finding cites is that the citers themselves are excessively erratic. If you quote the Talmud accurately and by folio, it's easy to find, but if you say the Bible says somewhere God helps those who help themselves then who can know what you're talking about? Then there is a second problem with finding cites, namely that there are a few words changed, and a few passages expurgated, but this is no more difficult than handling the Bible either; and in fact some expurgations were mandated by the Inquisition.
The medieval Zohar and the many commentaries are indeed hard to track, but they don't represent Judaism. If I go and say a Christian book says there is no hell, that's not Christianity. But in the 19th century many critics of Judaism (including Pranaitis of "Talmud Unmasked") lumped everything they heard or could find into long books of critiques that were divorced from context; and my quotes page traces how many of these were further made unfindable due to transcriptions from German, French, etc., and recompilation over time. The original authors often had manuscripts at hand that we have no idea how to find nowadays, meaning the originals have no reach whatsoever nowadays except via their being misquoted! So, overall, the disputation between everything ever said in Judaism and every criticism ever made in Christianity is indeed poorly organized in every century and still ongoing. But we can always assist the processing of that disputation here in small part.
Since the Talmud has faced variant readings, we do indeed need to use a little textual criticism to compare readings, just as with the Bible or any ancient text. But, even when we take the worst readings, they never amount to dogmatic Judaism, they only indicate trends in Jewish thought that come and go. We can learn from the worst of the trends, but we have no right to treat all modern Jews as following the extremes. It's appropriate to know how the variants may indicate an earlier text, but without direct evidence we can't invent a text that isn't extant simply because other things had other variants. For instance, Yeshu is never replaced with "the one whose memory shall be erased", that's a misunderstanding. It's always Yeshu, but in one instance it is said that Yeshu is an acronym for "may his name and his memory be erased", so that readers, if they wish, can think the one thought whenever they read the name Yeshu. But Yeshu is not Jesus's name, it's a nickname that wouldn't have been applied to him except possibly in one hill-country region of Judea. So having the facts is essential to process the criticism correctly.
I'm not prepared to discuss every page of "Talmud Unmasked" yet, but I've begun a collection, linked above, of the most egregious charges when placed in their right context. I agree entirely with OP on the point that the right understanding of these passages in context is essential to being able to object to facets of Talmudic Judaism. The problem is that the original objectors (among which Pranaitis was more balanced than average) overcompensated so much in the direction of castigation that their misattributions remain memetic today. It's true that there's an insularity in the Talmudic culture that appears debasing to outsiders, but that aspect is true of most races and religions and that is why we need the truth of Jesus as Messiah to remove such barriers. By misrepresenting the Talmud we only increase the barrier, challenging readers either to grow more racist than the Talmud is accused of being, or else to grow more sympathetic toward the Talmud in its having been misrepresented.