Dimensions are only an idea made by man kind to describe shapes or objects that lay on a certain number of axis, so I don't believe time has a dimension, because time is just a measurement relative to planetary rotation and orbit.
Philosophy aside, time is a very real thing and is persistent throughout the universe. However, a large number of things change the rate of it's passing. Our hours and minutes are determined by the rotations and movements of our planet, but that doesn't mean that all time is tied to those things. Notice in star trek how they use "Stardates" instead of a standard day system? Because days are arbitrary as far as universal time is concerned.
You are correct in your definition of dimension, at least in it's simplest sense. Generally time is percieved to have a single dimension, as a piece of string or a standard number line. going in two directions and nothing but those two directions. The concept of it being two-dimensional implies that our timelines wiggles around a deal and introduces the possibility of odd phenomena.
Note: This is my basic understanding of this topic. I do not have a major in this field nor have a read an excessive amount about this. Thus I may be completely and utterly wrong.
