Prashiddha Bista

Yes, a physical quantity can have magnitude and direction but still be a scalar if it doesn't obey the vector addition. An example is Electric Current which has magnitude and a fixed direction, but it does not follow vector laws of addition.

No, it is not necessary that a physical quantity that has magnitude and direction be a vector quantity.But yes a vector quantity should have magnitude and direction and apart from that, it should also follow vector laws of addition. One eg. for a quantity that has magnitude and direction but does not follow vector laws of addition is electric current.