If I see that three old answers of mine on the Linguistics sitehave all been downvoted today, is it reasonable to suspect somebody is stalking me?
It is indeed possible that someone was checking out your profile in particular rather than just, by coincidence, several questions you have been answering, but with a mere 3 downvotes, I would certainly not by worried about stalking. Someone was interested in who that Colin Fine guy is, scrolled a bit through your posts, disagreed with three of them, that's it. I'm almost sure I've done a similar thing once or twice before and I certainly didn't mean to stalk these users, just casually checking out on what they write and cast my votes as I would normally do.
That is possible: another alternative is that someone was reviewing a set of topics that you wrote on and disagreed with your answers. It depends how implausible it is that someone would encounter those answers.
Yes it is possible that somebody might be stalking. Another alternative is that somebody was looking at a set of tags, and they disagreed all your answers when they looked on the 3 questions that have your answers in it on each tag.