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The most common mistake is forgetting that a placement must satisfy the diagonals as well as the normal Sudoku rules.
No. The standard row, column and box rules still apply. The diagonals simply add another layer of restrictions.
Diagonal Sudoku adds the two main diagonals to the usual row, column and box rules. Every placement must satisfy both the grid and the diagonal restrictions.
Yes. Classic Sudoku logic still applies, but you also need to watch the two diagonals and the additional eliminations they create.
Start by looking at the diagonals and identifying cells that are already heavily restricted by rows, columns or boxes.