All right, hexes, I love it!

You're correct on points 1 and 2. And the same principle applies to hexes as in grids -- you're just adding or subtracting as needed. Using the 'Z' axis as defined in the chapter (namely, the roughly Northeast/Southwest diagonal axis on a two-dimensional hexagonal grid, not the up/down 'Z' axis used in the three-dimensional Cartesian coordinate system) is a little more complex, so first I'm going to answer the question: "What happens if you apply 2g in the -Y direction?"

When you're just using X (left-right) and Y (roughly Northwest/Southeast diagonal) axes on a hex grid, you can express any velocity in the same (X, Y) vector format. So if you start at (0,0), and apply 4 Thrust in the positive-X direction, your velocity will change to (4,0). At that point, if you apply 2 Thrust in the negative-Y direction, your velocity will change to (4,-2).

For the 'Z' axis, take a look at the "Using the Z Axis" section, and my personal recommendation is to use the second bullet point, translating 'Z' axis movement to X and Y equivalents -- any Thrust or velocity along the Z axis can be expressed as equivalent Thrust or velocity along both the X and Y axes simultaneously. So if you are starting at (0,0) on a hex grid, and apply 2 Thrust in the negative-Z direction, it's the same as applying 2 Thrust in the negative-X *and* negative-Y directions. Therefore, your new velocity would be (-2,-2). This may seem like you're applying a total of 4 Thrust (2 in the negative-X direction and 2 in the negative-Y direction, but that's just an artifact of how we count things for this third "axis".

Taking a more complex example, let's say you want thrust in the "South" direction, splitting the difference between the -Y and -Z directions. If you're starting at a velocity of (0,0), how do you apply 1 Thrust in the negative-Y direction, and 1 Thrust in the negative-Z direction? First, translate that negative-Z thrust into its X/Y equivalent, which will be (-1,-1). Then add the negative-Y thrust to that, resulting in (-1,-2). Taking a look at the X/Y/Z 3-axis diagram at the top left of page 172, you'll see that (-1,-2) (1 hex in the -X direction, 2 hexes in the -Y direction) will put you 2 hexes due "South" of the starting point.

So now let's say your velocity is (-1,-2) and the next turn you decide to apply 4 Thrust in the +Z direction. First translate that Z Thrust into X and Y equivalents, making it (4,4). Then add that to your existing velocity of (-1,-2), and your resulting net velocity will now be (3,2).