ABRIDGED: NGC5253 was previously studied by our group with the aim to elucidate in detail the starburst interaction processes. Some open issues regarding the 2D structure of the main properties of the ionized gas remain to be addressed. Using IFS data obtained with FLAMES, we derived 2D maps for different tracers of electron density (n_e), electron temperature (T_e) and ionization degree. The maps for n_e as traced by several line ratios are compatible with a 3D stratified view of the nebula with the highest n_e in the innermost layers and a decrease of n_e outwards. To our knowledge, this is the first time that a T_e map based on [SII] lines for an extragalactic object is presented. The joint interpretation of our two T_e maps is consistent with a T_e structure in 3D with higher temperatures close to the main ionizing source surrounded by a colder and more diffuse component. The highest ionization degree is found at the peak of emission for the gas with relatively high ionization in the main GHIIR and lower ionization degree delineating the more extended diffuse component. Abundances for O, Ne and Ar are constant over the mapped area within <0.1 dex. The mean 12+log(O/H) is 8.26 while the relative abundances of log(N/O), log(Ne/O) and log(Ar/O) were sim-1.32, -0.65 and -2.33, respectively. There are two locations with enhanced N/O. The first (log(N/O)sim-0.95) is associated to two super star clusters. The second (log(N/O)sim-1.17), reported here for the first time, is associated to two moderately massive (2-4x10^4 M_sun) and relatively old (sim10 Myr) clusters. A comparison of the N/O map with those produced by strong line methods supports the use of N2O2 over N2S2 in the search for chemical inhomogeneities within a galaxy. The results on the localized nitrogen enhancement were used to compile and discuss the factors that affect the complex relationship between Wolf-Rayet stars and N/O excess.
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