We study nuclear stopping in central collisions for heavy-ion induced reactions in the Fermi energy domain, between $15$ and $100$ A\,\textrm{MeV}. Using the large dataset of exclusive measurements provided by the $4\pi$ array \emph{INDRA}, we determine the relative degree of stopping as a function of system mass and bombarding energy. We show that the stopping can be directly related to the transport properties in the nuclear medium. By looking specifically at free nucleons (here protons), we present for the first time a comprehensive body of experimental results concerning the mean free path, the nucleon-nucleon cross-section and in-medium effects in nuclear matter. It is shown that the mean free path exhibits a maximum at $\lambda_{NN}=9.5 \pm 2$ \textrm{fm}, around $E_{inc}=35-40$ A\,\textrm{MeV} incident energy and decreases toward an asymptotic value $\lambda_{NN}= 4.5 \pm 1$ \textrm{fm} at $E_{inc} = 100$ A\,\textrm{MeV}. After accounting for Pauli blocking of elastic nucleon-nucleon collisions, it is shown that the effective in-medium \emph{NN} cross section is further reduced compared to the free value in this energy range. Therefore, in-medium effects cannot be neglected in the Fermi energy range. These results bring new fundamental inputs for microscopic descriptions of nuclear reactions in the Fermi energy domain.Read less <