Will Allah hold me accountable for a fatwa that I transmitted by mistake, after having misunderstood it from a website and not knowing of its error?

As long as you are not among those qualified to issue fatwas, you are not permitted to issue a fatwa merely by reading one. Instead, confine yourself to conveying the text of the fatwa only. Beware of attempting to deduce a ruling from another fatwa and applying analogy to it, even if you believe there is no difference between them, for that is the exclusive domain of those qualified to issue fatwas. There is no sin upon you if you did not intentionally err, according to the Almighty’s saying: "Our Lord, do not take us to task if we forget or make a mistake" (Al-Baqarah: 286), and His saying: "And there is no blame upon you for that in which you have erred, but [only for] what your hearts have intended" (Al-Ahzab: 5). However, you must rectify the matter and inform them of it to correct your mistake. You must also be deliberate when reading fatwas and ascertain their content, and avoid issuing fatwas as long as you are not qualified to do so.