No.
If you are studying waiting time, for example at a bank, the waiting time could be the dependent variable with the number of open windows as the independent variable.
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The horizontal axis is reserved for the independent variable in a function. Time is always an independent variable in time-based functions. However, duration can be dependent. It depends on what's being plotted.
There is no such quantity. Time is often cited as an example but it is always the dependent variable when studying the periodicity of pendulums, or waiting time in queues.
Time is often an independent variable.
the dependent variable changes with the independent variable. the independent variable only changes when changed by the experimenter. Time is usually an independent variable.
Time is the independent variable.