True. We don’t follow precedent. But to an extent, we use precedent to figure out the halacha, which is based in the Gemara and our brains.
Yes. But you see how that is something else entirely.
However, this isn’t entirely true. When there was semicha, a Beis Din had the power to actually be koveia halacha.
True, the precedent of the sanhedrin was much closer to the precedent of the common law.