It depends on what the domain and the range are. If the range is the positive integers, then the mapping is not even defined.
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yes
Yes and it will be a straight line intercepting y at -1 and parallel to the x axis
One half!
y = x - 3 is a linear function where for each x-value we find one and only one y-value.
It depends on the domain of y. If that is restricted to non-negative values, then the answer is yes. But if y is allowed to be negative, then the answer is no because then there are two values of y for each non-zero value of x.