Question

If n is a rational number then n2 is always less than n

Answer 1

That easiliy false. You can prove this by observing that all integers are, in particular, rational numbers. So, for instance, you can think of 4 as $\frac{4}{1}$, so $4 \in \mathbb{Z}\subset\mathbb{Q}$

And obviously, you have $4^2=16>4$

It is true that the square of every rational number between 0 and 1 is smaller than the number itself.

But since not all rational numbers are between 0 and 1, the general claim is false.