The answer depends entirely on what the question is.
If you want too know how far you can go while travelling at v kilometres per hour over a period of h hours, then the dependent variable is the distance.
If you want too know how long it would take you to go s kilometres when travelling at v kilometres per hour, then the dependent variable is the time.
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In simplest terms, a dependent variable is the a variable that depends on another variable.For example, if you are doing a biology lab, you may measure the length of time you leave something in acid with the change that it makes in the mass of an object. The change in mass is a variable, and it is dependent on the length of time you leave the object in the acid - so it is the dependent variable.
Typically the independent variable is plotted on the horizontal (x) axis. Usually time is an independent variable, and the other variables are dependent on time and other factors. In general, yes, plots involving time would show time as the x-axis.
A rate is a ratio which measures a certain variable in an amount of time. The most common rate would be distance / time (which measures speed).
It depends on how the variable is used. At its simplest, it would be a nominal or categorical value but, if used as part of a time series, it would be an ordinal variable.
The rate of change requires two variables. Usually some physical measure and time (or distance), and the rate of change is the difference in the physical variable per unit change in time (or distance). The question contains only one variable.