Scalar product

Consider the following statements:

(1) Dot product over vector addition is distributive

(2) Cross product over vector addition is distributive

(3) Cross product of vectors is associative

Which of the above statements is/are correct?

Consider the following statements:

(1) The cross product of two unit vectors is always a unit vector.

(2) The dot product of two unit vectors is always unity.

(3) The magnitude of sum of two unit vectors is always greater than the magnitude of their difference.

Which of the above statements are not correct?