The R and S are a maker's mark, but unfortunately, I don't know who that maker is.
Your ring is very old; likely pre-1900, and VERY cool to boot! I can't tell from the pictures, but they very well may be emeralds as you suggest. But you should also know that green doublets were very common in rings like yours. Doublets are what was used for a better simulated stone back then. They consist of a thin layer of usually garnet in this case, cemented onto a glass bottom.
Is it worth anything, you ask. Yes. But to a dealer, probably not much. Rings like these even in really good shape are surprisingly affordable. Your ring has a large amount of wear, but at least it appears like most of the prongs are still intact to some degree.
If you are at all sentimental, the ring is probably worth more to you than anyone else in the world. You could probably get the missing and chipped stones replaced without doing a major reconstruction of the ring and keep it as a family heirloom that could be worn occasionally. You would never want to make that an everyday wear ring any more than you would use a classic 80-year-old+ automobile for your everyday transportation.
Great ring! I hope you decide to restore and keep it!
