What is the ruling on taking financial payment for transcribing videoed prophetic hadiths into a Word file, and is that considered trading in religion? And is one who transcribes weak hadiths sinful if there will be someone who verifies their authenticity later?

There is no harm in taking a fee for writing and transmitting hadiths, because it is a wage and compensation for the effort expended in writing and transmission, and not trading with religion. There is no sin in writing weak hadiths, because the employer is the one responsible for editing the written material and distinguishing the weak from the authentic.