A rational number, by definition, is an integer divided by another integer (that's not equal to zero).
As for the integers themselves, for example [tex]3=\frac{3}{1}[/tex] we see that 3 is in fact an integer divided by another integer, so is a rational number as well. The same exact argument can be used for any whole number
Yes, the "whole numbers" is a subset of the rational numbers.
The answer to "will any whole number divided by any other whole number be a rational number" is "almost". Any whole number divided by any whole number except 0 is a rational number.