The convention for the Cartesian coordinate system is, the first number is the x coordinate, and the second number is the y coordinate. That's the order.
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If a set of ordered pairs is not a relation, the set can still be a function.
This kind of question usually accompanies a specific table of ordered pairs. The idea is that the ordered pairs take the form of (x, f(x)) where the first number of the ordered pair x, is a value of the variable for some equation. When that value is used in place of the variable in the equation, we can calculate a specific value. That calculated value appears as the second value of the ordered pair and is represented by f(x) above. Typically the equation is relatively simple, such as a linear equation or a quadratic equation. Therefore, in order to determine the equation, we have to know exactly what the ordered pairs are.
In general you cannot. Any set of ordered pairs can be a graph, a table, a diagram or relation. Any set of ordered pairs that is one-to-one or many-to-one can be an equation, function.
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No. For direct variation, any order pair with a 0 in it MUST be (0,0).