You guys seem to be getting the idea.
I really hate it ehen fil/TV get space physics wrong, which let's face it is most of the time. The prime offender is the movie Armageddon, it gets almost everything wrong (Just don't get me started!)
Dag'nabbit,
To compkletely represent the situation, you need facing, vector and speed as you rightly point out. Also you might need weapon direction if you're firing arcs are not fixed. To be perfect you would also need to know your current acceleration rate (unless you accelerate in discrete bursts).
Obviously all of these would be needed in 2 or 3 dimensions, however many you're working in.
El Cid,
I'm going to be really picky but traditionally in aircraft, and missile, technology. Forward is +x axis, positive yaw is a turn to the right (or starboard) and so motion to the right is usually considered +y axis. Therefore to maintain a right handed axis set, +z would be 'down'. The number of times in my work I have to remember higher altitude is a bigger negative number, it can make you go spare, it really can!
And as for our guest, Pottsbr, I like the quote, which is from Star Trek II, and is one of only a handful of occassions when ST universe uses 3-dimensionality of space, and besides that it's the best of the movies.
Here endeth the lesson
LBH