Yes, if it is described as such.
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It is an array with the same number of rows and columns.
A perfect square.
4th
I suppose you could refer to a two-dimensional array as a rectangular or square array (or as a jagged array of not all arrays within a given dimension have the same size). Table, grid or matrix may also be good synonyms for two-dimensional array, subject to the problem domain addressed with the algorithm.
I recently studied a magic square. It is a square that when each row, diagonal, horizontally, or vertically is added up, it equals the same positive integer.