The majority of known stars are taken from the Hipparcos Catalogue, a bit more than 110000 stars.
SpaceEngine doesn't have yet many standard planetarium tools, but they're in the TODO list. The recent implementation of analytical models for computing Solar System orbits it's a big leap in that direction.
As for accuracy, well it depends. I still giggle from time to time for this post (from the exoplanets news thread):
SpaceEngine goal is also portraying what we know about astronomical objects. It tries to convey the sheer vastness of known universe in a mid-range gaming computer, and wow, it does the job to methank you Vladimir, for all the help. Funny story, using spaceengine we even corrected some of NASA's early press release images, since we noticed that Orion on their images looked different to ours (ESO), from Trappist-1 point of view. I checked trappist-1 position on the catalogue files of SE and it all looked correct, so we prompted them, and upon checking they had their coordinates for Trappist-1 wrong (they were using Uniview), and then corrected it! ;)
So yes, thanks once again!

I'd say you definitely breathe Astronomy with SE, and every day a bit more to it. With a ludic experience too, even better a VR one... How much this can change your perception of science? For me it's like saying: This is the limit of the universe we know, feel it, touch it: What's yours, human?