1. It does...

2. \sqrt{7} + \sqrt{7} can NOT be denoted as \sqrt{7 + 7}.

3. Yes

4. Surely the denominator is just 1, so your whole fraction simplifies to \sqrt{n + 1} + \sqrt{n}...

5. Try converting 0.001222222222(repeated) to a fraction.

6. To teach us all how to write unambiguously...