Will I discover space stations through exploring

I can only definitively answer part (1), and that answer is:

Yes, once you have explored a system you retain that information and it shows on the System Map for you.

I understand from the game forums that the first players to survey a system get more income from doing so than later players - but that later players do get some (presumably this data is confirmation of the earlier surveyors' findings).

I recall from memories of statements by the developers (can't cite, sorry) that in the released game, systems that have been explored and see a lot of player traffic will eventually have space stations built and come under faction control. I don't know whether the faction that players sell the data to has influence on the faction that moves into the system.

Most of the populated space is near Sol. You can direct your ship towards Sol by moving towards the 0,0,0 coordinates on the Galaxy Map. Otherwise you might be able to find nearby populated systems on the Galaxy map by zooming out and playing with the View filters - anything with an Economy likely has a station.