Structural and magnetic properties of $\mathrm{Fe}(5\mathrm{nm})/\mathrm{Mn}{(t}_{\mathrm{Mn}})/\mathrm{Fe}(5\mathrm{nm})$ ${(t}_{\mathrm{Mn}}$ from 0.5 to 3.0 nm) sandwich structures, grown by molecular-beam epitaxy between 50 \ifmmode^\circ\else\textdegree\fi{}C and 150 \ifmmode^\circ\else\textdegree\fi{}C, were investigated using reflection high-energy electron diffraction (RHEED), x-ray-diffraction, M\"ossbauer spectroscopy, and magnetization measurements. Epitaxial bct-Mn structures only form for ${t}_{\mathrm{Mn}}<1\mathrm{nm},$ independently of the growth temperature. Room-temperature conversion electron M\"ossbauer spectra are composed of two magnetic components with in-plane magnetic moments. The first subspectrum has hyperfine parameters close to \ensuremath{\alpha}-Fe and is therefore associated with Fe atoms far from the interface regions. The second component, fitted with a hyperfine field (hf) distribution, has an isomer-shift value similar to \ensuremath{\alpha}-Fe and a maximum in the distribution curve at about 31 T. This subspectrum is related to the Fe atoms close to the Mn layer (interface regions). Low-field components in the hf distribution curves indicate the presence of Fe atoms or/and Fe clusters in the Mn spacers. An Fe-Mn alloy was observed for the samples grown for temperatures higher than or equal to 50 \ifmmode^\circ\else\textdegree\fi{}C and where the RHEED patterns show the presence of the \ensuremath{\alpha}-Mn phase. Magnetization data show that the Fe layers are ferromagnetically coupled for all trilayers prepared at substrate temperatures lower than 150 \ifmmode^\circ\else\textdegree\fi{}C. A noncollinear coupling was found for the trilayer with Mn thickness of 1 nm and grown at 150 \ifmmode^\circ\else\textdegree\fi{}C.