As for [5], see if you can come up with an example, where the linear system Ax = b1 + b2 is inconsistent. For starters, let b2 be the zero vector and think about cases where A is 2x2.

For [6], the rank of A is the maximum number of linearly independent columns of A. If the augmented matrix has the same rank, then the maximum number of linearly independent columns of the augmented system is the same as the maximum number of linearly independent columns of A. What does this tell you about the relation between the vector b and the columns of A?