I doubt the other systems exist in the demo for just that reason.

No to both questions.

I tried it the night before I got the full game. Steered my ship in a direction and left the computer on and came back a few hours later.
You just come to a barrier (if I remember it right 10000) but you don´t get to anywhere else. On the map you´ve only your blinking thing (like then your out of the map range - cause you are). You can see your distance if target a planet/station in the center of the system. Uhmm it´s really like a barrier - you don´t see anything, but your ship doesn´t gain any (youre at full cruise speed, display says this) further distance to any object behind you (e.g. there you come from).
Blubbered a little bit, sorry for my terrible English.

Nope...individual systems are seperate entities; there is no way to travel between them other than by jumpgate, jump hole, or mission change(i.e. the last few missions, which "magically" teleport you allll over the place). If they were all one big map, you wouldn't get that loading bar in the middle of system to system jumps.

Unfortunately, unlike the full game, the FL intro only has a single system, New York.

Reaper: $200,000,000.
Rockets: $100,000
The look on that pilot's face when you launch a full pod of screamers up his tailpipe: priceless