Sort of
Basically, during combat, docking and other non-distance-travelling, a ship in Elite: Dangerous follows a basic Newtonian physics flight model, but there are limits set to make dogfights possible that do make things somewhat like flying a plane in atmosphere.
The basic flight physics model is Newtonian [1] [2] with proper rigid body physics model, but there is a fly-by-wire system in your ship that constrains your angular and linear velocity to a common reference frame. This level of constraint on your ship cannot be disabled. This is specifically designed to make close-range tactical dogfighting possible. With a non-constrained newtonian physics model (no common reference frame, no top speeds, etc), instead of dogfighting with other ships you'd pass them quickly by as you exchange a few shots, and then never be able to catch up to them again ("jousting").
In addition to those constraints, there is a default of flight assist on that further limits your ship, so that your ship is moving in the same direction it is pointed, and so that you control a forward/backward throttle (speed setting) instead of directly controlling the forward/backward thrusters. It will use all available thrusters to perform the maneuver you want, even if you don't touch the controls for them. (in other words, pull back on the stick and your ship starts to point upwards, and both upward and forward thrusters are used to change your ship's movement to that new direction) It also seems to limit your non-forward movement speed more than it is without it. You can disable flight assist, enabling your ship to "skid" through turns (change the angle of the ship faster than the direction of motion changes), fly backwards, etc.
There's also a separately optional "rotational correction" feature, that sets your ship's frame of reference to the rotating station's rotating reference when you're docking in a rotating station. Landing inside of a rotation space station without that would be very tricky.
While you do have a full six degrees of freedom, most ships have significantly more forward thrust/throttle than any other thrust direction, and very limited yaw. This means that if you want to turn left, you'll find a direct leftward yaw to be very slow, and instead will want to either roll left and pitch up, or roll right and pitch down. Because of the cockpit design, most people would find turning left with a left roll easier to work with. You don't bank, however, you would roll a full 90 degrees and pitch. Or you might do some roll, pitch and yaw all at once to get turned left as fast as possible, and that could look a bit like banking. Depending on your controller set up, you might want a certain amount of "yaw into roll", which is an option in the settings.
To specifically answer the questions in your last paragraph: with flight assist off: You don't really have "throttle" anymore, you have thruster controls. If you leave the "throttle" on, you'll eventually reach your top speed. If you want to stop moving, you have to provide the correct amount of thrust in the opposite direction. When you start to rotate in one direction, you have to apply counter-rotation thrusters in the same amount to stop the rotation.
Your ship's power source is a hydrogen fusion reactor, and I believe the thrusters are ion drives or something like that. Basically that means while you do use fuel, the fuel usage is fairly constant in newtonian flight, and the mass reduction is very slow. In other words: not at all like real rockets where fuel mass is a huge deal.
In addition to the basic newtonian physics flight that you use for combat, docking, etc, there is a "frame shift drive" that allows for faster than light "supercruising" within a system and fairly instantaneous jumps between systems. One further non-realistic detail is that you cannot move between systems without using the jump facility of your frame shift drive. If you try to "supercruise" to a star in another system, there simply won't be anything there when you get there.
Most players use flight assist on most of the time, because flight assist off is hard. Experienced players will briefly toggle flight assist off to facilitate faster turning in a dogfight, or other maneuvers. Some of that can actually be accomplished by using vertical thrusters during the turn, which pretty much tells your flight assist computer that you want to skid into the turn and then lets you rotate a bit faster.
Here is a nice video tutorial on the differences between flight assist on and off:
Here are a set of Elite: Dangerous tutorial videos that include several on flying with flight assist off: https://www.youtube.com/playlist?list=PLU396ir67nHiJwEswBslJORR9YFG7qRU2
And Isinona has a whole "Flight Assist Off" series of videos, where he shows his various exploits in E:D, always flying with flight assist off: https://www.youtube.com/user/Isinona
