Going to skip over feasibility and just go to the social impacts. One of the odder aspects of this question is you can somewhat draw on Earths population for examples here...prior to electricity, human light did not block out the night sky and they were significantly more noticeable than today. Stars are at the core of our belief structure (In Roman times, the stars were gods poking holes in the night sky to see down). They were heavily studied and entire lifetimes were devoted to tracking them and their movements (one effort to locate god in the stars actually managed to pinpoint a location in which the majority of stars swirled around...as we later discover, the area pinpointed was a decent approximation for the super massive black hole at the center of the milky way). When you have a lifetime to dedicate to watching and tracking star movement, it's amazing the conclusions you can come to.
Today, we have light 'pollution' and the majority of humans are unable to see all but the brightest stars in the sky....we heavily neglect them today and (in my opinion of course) have lost our connection to them and with it, our desire to reach for them. Leaves us stuck in our small petty worlds blissfully unaware of the grandeur of the universe.
Early humans actually read a significant amount of information from our evening sky and the proof of this is pretty readily available. In whats now known as http://blog.world-mysteries.com/science/ancient-time-keepers-archaeoastronomy/ Archaeoastronomy (how ancient cultures viewed the stars) we piece together how ancient cultures related themselves to the stars, and it's not a big surprise how heavily the stars influenced our early culture. The earliest is mentioned in the link here, astronomically aligned stones placed in Egypt date back between 6400bc and 4900bc. Wonders of the world such as the Pyramids and Stonehenge directly relate to star positions and tracing the flow of time using the stars. The Mayan calendar gives hints that the Mayan's were capable of reading the Earths 26'000 year wobble cycle from staring at the stars as well.
Most planets are names are directly derived from Gods (or vice versa?)...the planets are significantly brighter in the night sky and move more readily, lending themselves to be called the greater god as they wandered through the night sky watching humanity below.
In my opinion, we start heavily watching the stars when Agriculture began gaining prominence as it was our first heavy tie to the seasonal calendar...when do you plant? when do you harvest? How much longer until our next rainy season? A lot of this information is exceedingly trivial to today's humans as there's an app for it I'm sure, but to early humans this information could really only be discerned from watching the stars.
And it's these points that your society will have to address as major changes over us:
1) I'll contend much of early Polytheistic religion directly stems from our star gazing and thinking those lights were staring back down at us, watching and judging. Without this, I'm thinking nature is your most likely place to find their early images of a god and their belief structure.
2) How do they tell time? Day to Day sure, the sun works...but how do you know when a full year has passed without the stars in the night time sky returning to where they started the year before? They'll have to come up with something semi-unique here as our ancestors almost exclusively used the sky to know when they should plant their fields, when the next winter was, and so on.
3) How do you arrive at a heliocentric view of the solar system? Would they be prone to thinking the world is flat far longer than we were (should point out that as a species, our first heliocentric image is early greek)...the positioning of planets, stars, and the sun give away (with enough study) that the earth orbits the sun. Without the stars to tell them, how do they figure out the Earth isn't flat?
4) Directions are what? Nothing gives away north prior to magnetism outside of the stars...the seasonal fluctuations means the sun isn't a good guide. Egyptians used rivers (there word for north was 'downstream nile'...and this created confusion when they encounters a east west flowing river). North East South West is determined by the stars...what do they use?
I've gotta dispute your one question though...ancient records from billions of years ago when the stars exist aren't going to be there anymore. If your planet is earth like, odds are the continents have drifted around, sunk into the earth, and have been pushed back up...the land wouldn't even be recognizable as what it once was billions of years ago. No record of billions of years ago would exist, so I'm having problems seeing 'ancient text books' or photographs existing to show that there was once a starry sky.