The time it takes depends on the distance, also the speed of the ship but for an outpost ship i'd say if it's a few sectors away maybe a few minutes.
The flashing light is the star, the bars next to it are how many planets in that sector. The bars will fill up brightly if you own a planet(s) in that sector, and darkly if someone else owns a planet(s) in that sector.
There are a lot of empty sectors, the vast nothingness of space. Also you won't see outside of your one sector grid around your home sector until you send probes out to explore.