The chemical composition and the magnetic structure of individual La_0.7Sr_0.3MnO₃ (LSMO) ferromagnetic manganite epitaxial nanostructures less than 200 nm in width are explored using Photoemission Electron Microscopy (PEEM). X-ray absorption spectra (XAS) provide separate information on the surface and the bulk composition of the nanoislands and give evidence of Mn²⁺ present on the surface of otherwise stoichiometric nanostructures. Ferromagnetic domains less than 70 nm are resolved using X-ray magnetic circular dichroism (XMCD), which allows for the detection of magnetic vortex states in both (001)_LSMO square and (111)_LSMO triangular manganite nanoislands. The evolution of single nanostructures under an in-plane magnetic field is seen to depend on the specific nanoisland size and geometry. In particular, PEEM XMCD imaging allows detecting opposite chiralities as well as a variety of magnetization behaviors for different nanoislands.