For example, if a newspaper wanted to publish letters and assure their readers of the writer’s authenticity, would they have been able to reproduce the letter and signature as a picture/lithograph in the newspaper? The 18th century equivalent of a scanned document appearing in a paper, I suppose.
Yes. What they could do is reproduce the letter as an image, done by a good engraver. I have seen books from the XVII and XVIII century that reproduce manuscript fragments, such as manuals on paleography like the Bibliotheca de la Polygraphia Española, linked here, where you can see accurate repoductions of many manuscripts, epigraphic inscriptions, and coins.