It is customary to use only positive or zero values. Of course, a vector with a negative value would be equivalent to a positive vector in the opposite direction.
No.
No, the value can't be negative because magnitude of a vector is just how long it is regardless of its direction. :-)
Vectors have magnitude and direction. The magnitude is always a positive number.
The magnitude of a vector is always treated as non negative and the minus sign indicates the reversal of that vector through an angle of 180 degree.