Yes, it's possible.
No, it's not possible.

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Since every cell is at least $1$ and at most $3$ , the sum of every row/column/diagonal is at least $100$ and at most $300$ . So there are $201$ possible sums (all the natural numbers between $100$ and $300$ ).

But since there are $100$ rows, $100$ columns and $2$ diagonals we need at least $202$ different sums, so $\boxed{\text{it's not possible}}$