I don't play a Stone Elf outside of a particular NPC, but I can help a bit, I think?
Stone Elves have emotions just like everyone else, they just don't display them openly to anyone else; you can be madly in love with someone or hate their guts, but you'll still hold the same neutral expression. Think of your emotions like your butt: everyone's got one, and some of them are very nice, but it's considered proper to keep it covered up in public.
Remember that there are a lot of ways you can make it known how you feel about something that don't have anything to do with an emotionally neutral face. Simply walking away can be used to show displeasure, offering to help people with their problems is a good way of showing you care about them, and so on. Even using particular words can change the entire tone of a conversation, so if you've got a big vocabulary, put it to good use.
About the only time it's really acceptable for a Stone Elf to show emotion is when they're doing a mental link with another Stone Elf, and that's usually a highly intimate thing for them, so you probably won't be doing it often; even then, it's entirely in your minds, so no one else is privy to it.
One thing you might find is that people get confused or stressed out after interacting with you for extended periods of time, because most people read body language subconsciously, and when we can't use facial expressions to read emotions, it tends to make us uneasy; it's one reason why masks are a popular tool to mark someone as a villain in visual media.
It won't be nearly as bad if you've been with the chapter for a while and people have gotten to know you, or if there are other Stone Elves you can group up with.