Let's consider a closed and oriented 4-manifold $M_4$ and denote $H_2(M_4,\mathbb{Z})$ as the homology group of 2-cycles and $Q_{M_4}(S_{A},S_{B})$ as the symmetric intersection pairing between 2-cycles $S_{A},S_{B} \in H_2(M_4,\mathbb{Z})$. I was told that by linearity the intersection form will always vanish when one of the 2-cycle is a torsion 2-cycle. I think the proof is the follows, if $S_{C}$ is a torsion 2-cycle such that $r S_{C}$ is shrinkable, then by linearity $r Q_{M_4}(S_{C},*) = Q_{M_4}(rS_{C},*) = 0$ and therefore $Q_{M_4}(S_{C},*)=0$.
My first question is the following. From geometry, the intersection pairing counts the number of the intersecting points between two 2-cycles. Does it mean there is no intersection between the torsion 2-cycle $S_{C}$ with any other 2-cycles in $H_2(M_4,\mathbb{Z})$? I found it difficult to imagine that geometrically.
Another related question is about torsion linking number, see the Wikipedia page https://en.wikipedia.org/wiki/Poincar%C3%A9_duality#Bilinear_pairings_formulation. It tells me on the 4-manifold $M_4$, there exists a duality pairing among the free part of $H_2$, which is nothing but the intersection pairing:
\begin{equation} Q_{M_4}:fH_2(M_4,\mathbb{Z}) \times fH_2(M_4,\mathbb{Z})\rightarrow\mathbb{Z}, \end{equation} and another duality pairing among the torsion part, \begin{equation} \widetilde{Q}_{M_4}:\tau H_2(M_4,\mathbb{Z})\times\tau H_1(M_4,\mathbb{Z})\rightarrow \mathbb{Q}/\mathbb{Z}, \end{equation} where $\mathbb{Q}/\mathbb{Z}$ is the quotient of rationals by the integers. For torsion 1-cycle $\alpha \in H_1(M_4,\mathbb{Z})$ such that $n\alpha$ is the boundary of a surface $S_{\alpha}$, this pairing is effectively calculated by counting the intersection number between $S_{\alpha}$ with the other torsion 2-cycles.
My second question is, is there any intersection between the 2-surface $S_{\alpha}$ constructed above with the free part of the 2-cycles? Or in other words, can I treat $Q_{M_4}$ and $\widetilde{Q}_{M_4}$ as two independent pairings without any mixing?
Thank you!