Morphisms of abelian variety and torus in additive group

Question

let $A$ be an abelian variety and $T$ be an algebraic torus over a field $k$; furthermore denote with $\mathbb G_a$ the additive group over $k$, i.e. just the affine space.

Why does then hold

(i) $Hom(T, \mathbb G_a)=0$

(ii) $Hom(A, \mathbb G_a)=0$

(iii) $Ext^1(T, \mathbb G_a)=0$,

if the hom groups denote really homomorphisms of group schemes?

Thank you