It is not true: consider the exact sequence of abelian groups $$0 \longrightarrow \mathbb{Z} \xrightarrow{x\mapsto 3x} \mathbb{Z} \xrightarrow{x\mapsto [x]_3} \mathbb{Z}/3 \longrightarrow 0 \quad$$ and note that the only homomorphism $\mathbb{Z}/3 \rightarrow \mathbb{Z}$ is the zero one. So the sequence does not split.
3. The sequence $0\rightarrow A \xrightarrow{q} B \xrightarrow{r} C\rightarrow 0$ and the canonical one $0\rightarrow A \xrightarrow{i} A \oplus C \xrightarrow{\pi} C\rightarrow 0$ are isomorphic (with the identities on A and on C).
It is not true: consider the exact sequence of abelian groups $$0 \longrightarrow \mathbb{Z} \xrightarrow{x\mapsto 3x} \mathbb{Z} \xrightarrow{x\mapsto [x]_3} \mathbb{Z}/3 \longrightarrow 0 \quad$$ and note that the only homomorphism $\mathbb{Z}/3 \rightarrow \mathbb{Z}$ is the zero one. So the sequence does not split.