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the dependent variable changes with the independent variable. the independent variable only changes when changed by the experimenter. Time is usually an independent variable.
Not necessarily. It will be if it is the only independent variable in the system.
In most real life cases, limiting an experiment to only one independent variable makes the whole experiment a waste of time. More often than not there are several independent variables.
The x variable, of course! If there are only two variables then the independent variable, if one exists, should be plotted on the x-axis.