Zero vector has zero value in the given vector space. So, it is different from zero scalar. Zero vector is additive identity of the given vector space whereas zero scalar is not. I do understand this academic distinction. But I still have following $2$ doubts.
(i) In one dimensional space, is zero scalar same as to zero vector?
According to me - NO. In $1D$ space, the vectors may be expressed in real number notation (instead of matrix notation) where absolute value of real number indicates magnitude and sign indicated direction. Then, we are using 'real number notation' to represent not a real number, but a vector in $1D$. What we represent is not real number. So, a zero vector in $1D$ space is indeed expressed as $0$ in 'real number notation'. However it is not representing the real number zero (which is member of set of real numbers) but representing zero vector (which is a member of vectors in 1D space). So, in $1D$ space, a zero vector may be represented by number $0$. But it is not the real number $0$.
Analogy -: A directed segment represents a vector. It is not a vector.
(ii) Is zero speed same as zero velocity? In general, if we define a scalar quantity $Q_1$ which is magnitude of a vector quantity $Q_2$, then is zero $Q_1$ same as zero $Q_2$?
According to me - NO. When speed is zero, then the velocity is zero and vice-versa. However, zero speed is not equal to zero velocity.