Squaring mathematical operations.

what is the mathematical term used to refer to operations like 1x1, 2x2, 3x3, 4x4, 5x5, etc

The mathematical term used to refer to operations like 1x1, 2x2, 3x3, 4x4, 5x5, etc is "squaring."

And the result of these expressions are called "square numbers," correct?

Yes, that is correct. The result of these expressions, 1x1, 2x2, 3x3, 4x4, 5x5, etc are called "square numbers" or "perfect squares" because they are the result of squaring a number.