Different aspects of the structure-magnetism and morphology-magnetism correlation in the ultrathin limit are studied in epitaxial Fe films grown on MgO(001). In the initial stages of growth the presence of substrate steps, intrinsically higher than an Fe atomic layer, prevent the connection between Fe islands and hence the formation of large volume magnetic regions. This is proposed as an explanation to the superparamagnetic nature of ultrathin Fe films grown on MgO in addition to the usually considered islanded, or Vollmer-Weber, growth. Using this model, we explain the observed transition from superparamagnetism to ferromagnetism for Fe coverages above 3 monolayers (ML). However, even though ferromagnetism and magnetocrystalline anisotropy are observed for 4 ML, complete coverage of the MgO substrate by the Fe ultrathin films only occurs around 6 ML as determined by polar Kerr spectra and simulations that consider different coverage situations. In annealed 3.5 ML Fe films, shape or configurational anisotropy dominates the intrinsic magnetocrystalline anisotropy, due to an annealing induced continuous to islanded morphological transition. A small interface anisotropy in thicker films is observed, probably due to dislocations observed at the Fe¿MgO(001) interface.