Poly(N-isopropylacrylamide) (pNIPAM) microgels are soft and deformable particles, which can adsorb at liquid interfaces. In the present paper, we study the two-dimensional organization of charged and quasi-neutral microgels with different cross-linking densities, under compression at the air-water interface and the transfer of the microgel monolayer onto a solid substrate at different surface pressures. At low cross-linking densities, the microgels form highly ordered hexagonal lattices on the solid substrate over large areas, with a unique lattice parameter that decreases continuously as the surface pressure increases. We thus prove that the microgel conformation evolves at the air-water interface. The microgels undergo a continuous transition from a highly flattened state at low surface coverage, where the maximal polymer segments are adsorbed at the interface, to entangled flattened microgels, and finally the thickening of the layer up to a dense hydrogel layer of compacted microgels. Moreover, two batches of microgels, with and without charges, are compared. The contribution of electrostatic interactions is assessed via changing the charge density of the microgels or modulating the Debye length. In both cases, electrostatics does not change the lattice parameter, meaning that, despite the microgel different swelling ratio, charges do not affect neither interactions between particles at the interface nor microgels adsorption. Conversely, the cross-linking density has a strong impact on microgel packing at the interface: increasing the cross-linking density strongly decreases the extent of microgel flattening and promotes the occurrence of coexisting hexagonally ordered domains with different lattice parameters.