More than you ever wanted to know about The Millenium Falcon.
Contrary to what is presented in the video, I would expect redundant systems in any kind of spacecraft. Nothing is mentioned of heat shielding for re-entry, although if you could slow a craft to a near stop then you wouldn't need it.
Even if we could create and store antimatter, which would be the most compact fuel possible, it would still take an enormous amount of fuel to continuously accelerate a craft all the way to the center of the Milky Way Galaxy. Reaching anywhere near the speed of light takes several times more mass of antimatter than the mass of the ship.