I just started doing more-or-less the same in Codorain (close to the high tech station of Leesti). Not sure I'd get a permit to an Empire system as I'm far removed from the 'main' Empire worlds. The Empire capital is in Achenar, so perhaps the system around could be regarded as core systems.
Space is huge, 2500 commanders is no guarantee you'll see them. Played last night for 4 hours, didn't see anyone in the area around me (working on my Empire rank in Codorain for the privilege to one day buy a Imperial Clipper).
Kepler-186 is a M1-type dwarf star, located 492 ± 59 light years away in the constellation of Cygnus. It's the star with planets orbiting it, with one of them in the goldylocks zone.
Yes this is purely PVE, the only place you may engage in PVP is warzones if you pick the opposite faction. (although if you'd ask me nicely I'd not target you there either).