Every time. The sum of two rational numbers MUST be a rational number.
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Suppose the two rational numbers are x and y.Then (ax + by)/(a+b) where a and b are any positive numbers will be a number between x and y.
Find the arithmetic average of the two rational numbers. It will be a rational number and will be between the two numbers.
For two rational numbers select any terminating or repeating decimal number which starts with 2.10 and for irrational numbers you require a non-terminating, non-repeating decimal which also starts with 2.10.
Yes, as long as the two nonzero numbers are themselves rational. (Since a rational number is any number that can be expressed as the quotient of two rational numbers, or any number that can be written as a fraction using only rational numbers.) If one of the nonzero numbers is not rational, the quotient will most likely be irrational.