Depends on which demo you played. It may have been the 1070 demo or the 1100 demo (which is current).
The UI did change somewhat between 1070 and 1100; mostly presentation wise. Functionally it's the same system with a few tweaks; e.g. when you zoom to an object now it'll keep the same distance between you and the camera as there was previous I believe. I did rework it to make much more information exposed and at-a-glance however. If your object information panel had a nebula in the background and a representation of the object you had selected on it, you were playing the 1100 demo.
I'm unsure what to make of your ships getting stuck inside a star; they should be pushed out by the collision system unless the ship fought back with very powerful thrust. Even then, it would be 'bouncing' into and out of the surface, not stuck inside. It also would only occur on moving to a Star, as it's attempting to reach a point near the star's center but is unable due to the enormity of the star's surface. In summary: No idea what's going on there; no idea how they even got stuck inside in the first place.
Most unexpected behaviors I expect a player would encounter from ships' AI settings and the player not being aware of those settings. For example, deploy a Cruiser without looking at its blueprint and you may find it prefers targets between 4 and 8 scale, even late-game where the average ship scale might be 1.2k; resulting in it going after "fighters" in mid-game as large as it is before the bigger fish. Or that your scouts decide to leave hostile systems or etc.
Not to say ships can't behave unexpectedly on their own. Movement, for instance: the movement solution isn't perfect and a number of steps can be taken to reduce its imperfection. Ships can go beyond their intended 0-velocity point during their deceleration phase, resulting in a 'slingshot' effect, but the problem is augmented if you're above normal speed. Groups of ships also can perform aberrantly when moved as a cluster; moving a group of ships tends to result in a more accurate stop than a fleet of the same ships moving over great distance.
Finally, having less than X ships in your game, where X is the limit of ships your computer can support before beginning to slow the game down will reduce a significant number of problems that might arise (ships suddenly losing power and dying, etc.). Unfortunately, the only way to know what X is is to run the game and approximate how many ships are in the galaxy at the time it slowed down. I'd say with modern hardware start with 1000 and adjust from there.
On Blueprints: The looks of a blueprint (read: where subsystems are placed) do not change the ship. It is what the ship has aboard that changes its appearance. Combat ships by and large go off the same 'line' of model; if a ship has a weapon system and no special other system, and has some means of propulsion, it's a combat model.
Adding special subsystems, such as a ShipBay or a Colonizer will give the ship an appearance representing those subsystems (A carrier and colony ship, respectively). Were there enough models to all possible types of ships they would roughly facsimile your blueprint. Unfortunately we were unable to obtain enough art for the ships to do so. Modders can certainly achieve full approximation for nearly any 'type' of ship; it's not the game's fault it doesn't have variety in ship design. Our lack of money and staff that did that, unfortunately.
Differences between full and demo: Mainly the addition of more types of subsytems, additional research options, multiplayer, the removal of the ship size cap, the ability to mod and run more than light substitution mods, more music, some additional planetary constructions, and our gratitude. The long and short of it being: If you like the demo, you'll like the full game more. If you didn't like the demo, you probably wouldn't like the full game.
We wanted our demo to represent the end product, and so (we hope) it does.
