Why shuffling by picking random position in all array instead of a part is not correct
Suppose that the array has length $n$. Since you are making $n$ random choices of numbers from 1 to $n$, the probability to obtain any specific permutation is of the form $A/n^n$, for some integer $A$. Therefore your algorithm could work only if $n^n/n!$ is an integer, which is only the case when $n \leq 2$.

More concretely, if you shuffle the array $1,2,3$, then you get the following results:
$$
\begin{array}{c|c}
\text{array} &amp; \text{probability} \\\hline
1,2,3 &amp; 4/27 \\
1,3,2 &amp; 5/27 \\
2,1,3 &amp; 5/27 \\
2,3,1 &amp; 5/27 \\
3,1,2 &amp; 4/27 \\
3,2,1 &amp; 4/27 
\end{array}
$$