To look at the various planets in the system you're in, select the orbital view (F2 in FE2, F6 in FFE) from the navigation screen.
In FE2 you can also see (and lock on) the ships in the system as colorful dots.
I also recommend doing all kinds of stuff, like landing on uninhabited planets like methane worlds, entering the atmospheres of gas giants and admiring the rings above their seas of clouds (best in FE2), landing on asteroidal bodies (FFE), visiting Canopus 1, flying by a white dwarf, putting your ship in (more or less) stable orbit around a planet, etc.
Of course, this kind of stuff requires decent manual flight skills.
As far as asteroids etc. are concerned, I think you just have to bump into them!
This reminds me of one of my flights.
I was doing about 4000km/s when I was ambushed by pirates. I quickly dispatched the attackers, but noticed some odd points of lights blinking around the ship. Puzzled and quite disoriented I stared at them not knowing what they were. Suddenly a huge wall of rock flashed by the side of my ship, then, in a blink of an eye disappeared into infinity behind the aft. The rest of the trip was uneventful, although I felt a bit nervous, having realized that I had just flown through an asteroid field and barely even noticed that - had I even scrapped one of these chunks of space debris the inhabitants of the system would be able to read by the light of the explosion for good several minutes. Of course, when you're hurtling through the system at 4000km/s there is little you can do to avoid collisions - you can only put your ship on autopilot and put your trust in the sparsity of any asteroid fields you may, unknowingly, buzz through.