yes to all that but its a little more complex because of the intensity problem.
Actually that gives me a way to explain it
When you look at a normal bitmap you have two dimensions but you also have a color at each pixel location.
So to describe a bitmap pixel by pixel you need
X location, Y location and Color of pixel
Now lets imagine we had a 3D TV or Hologram lets take the classic stars wars one
Ok to describe Leia as a 3D we need 4 numbers
X location, Y location, Z location and color of pixel
So to make a colored 3D image you need 4 dimensions in that case 3 are physical and 1 is a color or intensity if in greyscale.
So if you want to call it 3D + color that is the same as we call it 3D + time so we avoid calling it 4D to stop this problem
That is as near as I am probably going to get you to understanding why you will need 4 dimensions and I don't mind if you object to calling the last one a dimension so 3D + something is fine to me.