No. "Natural" numbers are the counting numbers, otherwise known
as the positive integers. They are all rational.
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Not always. For example sqrt(2) and 1/sqrt(2) are both irrational, but their product is the rational number 1.
Yes. A number can be either rational or irrational, but never both; otherwise there would be an inherent contradiction.
No number can be both rational and irrational. And, at the level that you must be for you to need to ask that question, a number must be either rational or irrational (ie not neither). 0.555555 is rational.
There is no such thing as a number that is both rational and irrational. By definition, every number is either rational or irrational.
' e ' . . . the base of natural logs