>>Time is not THE fourth dimension, but just yet another dimension that is commonly unified with the spatial dimension for convenience in physics.<<
Indeed, time is not the 4th dimension, the 4th dimension is external space - it includes four things: width, length, volume, time. Commonly it is just known as space-time.
A 2D can exist in a 3D world. The 2D would consist of only width and length - there is no observable volume. Think of when you watch a cartoon, or look a line you've drawn on a piece of paper.