3 variables
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Most science experiments will have two independent variables. Fundamentally, an experiment will want as few variables as possible for better results.
Infinitely many.
Explanatory (or independent) variables are variables such that changes in their value are thought to cause changes in the "dependent" variables.
An equation with absolute values instead of simple variables has twice as many solutions as an otherwise identical equation with simple variables, because every absolute value has both a negative and a positive counterpart.
You isolate variables in math because the point of an equation is to solve for the variables. By isolating the variables you have learned what that variable stands for and thus solved the equation.