Rational: yes. Natural: no.
5 = 5/1 is a rational number
As a number which can be expressed as a fraction, 1/2 is a rational number.
No, it cannot. The product of a rational and irrational is always irrational. And half a number is equivalent to multiplication by 0.5
Yes, -1/2 is a rational number
There is no such number. If any number laid claim to being the smallest rational number its claim could be challenged by half that number - which would also be rational and, obviously smaller. And the claim of that number could be challenged by half that number, and so on.
I am rational, but not a number. This statement is therefore half correct.