Yes, sometimes they can. If you react or comment in a way that shows you already know what's going to happen in the story, it might give it away. Also, if you mention details that are not obvious on a first watch, people could suspect that you've rewatched it.
Well, it depends. If you are really good at hiding your reactions, then people may not be able to tell. However, if you keep referring back to specific parts of the story that are not typically noticed on the first go - like a small detail in the background or a particular line of dialogue - then it's likely that others will figure out you've rewatched it. Another factor could be your enthusiasm. If you seem overly excited about a story you've already seen before, it might raise suspicions.