I haven't bought this yet. Currently playing through Atom and enjoying it with my character who I named - Artyom. Possibly will get Encase next if it has a good story. So the premise as I understand it -

There is a mysterious alien dome that appears somewhere in the 70s. A corporation in charge sets up nearby in order to research it. Humans can go in, but can't leave. So my first question is, I guess, objects and communications can go through in and out?

I can't find any information on the actual object of the game like what the main story is about. So humans have been inside the dome for about 5 years or so, and have their own sort of society going on in there? And that is what you explore? Or am I just way off on this? I don't understand. Thanks.

You've got it mostly right. The society inside is mostly run by the corp though. There's commerce so supplies are sent in and weird artifacts and research are sent out. Also, new staff is continuously sent in (which is where your player character comes from).

Also going into the Dome isn't quite what you think it is. it isn't just a building or structure you enter and work, it's much more than that which you will find out as you play, so no spoilers.. the BASIC idea when you start is that you are being sent into the DOME to work and do stuff, but that is just the beginning of the story.