The correct statement/statements is/are:

(1) ${\mathrm{d}}_{\mathrm{nearest}}\mathrm{O}.\mathrm{V}=\frac{\mathrm{a}}{\sqrt{2}}=\frac{2\sqrt{2}\mathrm{r}}{\sqrt{2}}=2\mathrm{r}$ (correct)

(2) 

(correct)

(3) ${\mathrm{d}}_{\mathrm{O}.\mathrm{V}\&\mathrm{T}.\mathrm{V}\mathrm{nearest}}=\frac{\sqrt{3}\mathrm{a}}{4}=\frac{\sqrt{3}}{4}\times 2\sqrt{2}\mathrm{r}=\sqrt{\frac{3}{2}}\mathrm{r}$ (correct)

(4) 

(4) $\mathrm{a}-2\mathrm{r}=2\sqrt{2}\mathrm{r}-2\mathrm{r}=2\left(\sqrt{2}-1\right)\mathrm{r}$ (Correct)