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Y=k/x where k is the constant of proportionality is an example of indirect or inverse variation. They are the same thing.
direct means it stays the same while inverse means it will change.
Yes.
In general the function and it inverse are not the same and do not have the same graph. If we look at a special function f(x)=x, it is equal to its inverse and the graph is the same. Think of the inverse of a function as changing all the x's to y's and vice versa. Well, in the function f(x)=x, all the x's are already y's and vice versa so it is its own invese.
A number and its multiplicative inverse have the same sign. So if one is negative, so is the other.