How can we believe and trust censored Bibles?

First of all, as others said, the Bible is a book composed of many books and letters written by many people over an incredibly vast span of time. Consistency is almost impossible. But, for what it's worth, where does the Bible say "that no one should make a dare to edit or correct" it?

I believe you are referring to Revelations which is, arguably, one of the oldest youngest if not the oldest youngest book in the canon (I don't remember for sure but I believe it is) and also not universally appreciated. Luther famously criticized Revelations, and I think rightly so. There was also some contention at the time of canonization in Nicea around Revelations. So, just because one book says it, doesn't mean it's the final word on the issue. There are Christians that don't see much weight or value in Revelations. I certainly don't, I don't believe it's an eschatological text revealed by God. I think the only way Revelations makes sense is to read it as an historical text and critique of Nero that was written post hoc to rationalize and comfort Christians for what they suffered by explaining that they will soon be rewarded for their faith because they are in "end times". Of course, we now know, thousands of years later, that they weren't.

Besides, I'm not entirely sure I know what you mean by "edited" or what "life" you're referring to, although I'm assuming you're talking about Jesus. Have you read the Scriptures in their original languages? I have at least read and translated the Christian Scriptures in and from Greek, and they need editing. It's not possible to have a transliteration of it that reads well, it takes some finesse and art. Even the Scriptures in the Greek are compiled from different manuscripts and codices because there often are errors or damages in manuscripts so you can't just find the one "Gospel of Marx" manuscript, for example, and use it to translate it perfectly. You need to find several to get the whole story of one gospel together and then translate them into a single text, so you're using several sources to put the story together in Greek and then translate into a different language thousands of years later. Naturally, this creates issues and makes it so that the Bible isn't an unaltered text in its final form. Unless you read it in its original language, this is unavoidable—and, as I said, even if you do read it in Greek, you will still have an "edited" text.

Does it matter? I think it creates issues and one should be able to critically examine these textual criticisms in order to form a better picture of the origins of their belief and better parse what and how to believe, but I don't think editing or inconsistencies inherently invalidate Christianity nor Judaism.