The electronic structure and characteristics of Fe 3d valence states of iron-chalcogenide Fe(1.01)Se superconductors under pressure were probed with x-ray absorption spectroscopy and resonant x-ray emission spectroscopy (RXES). The intensity of the pre-edge peak at ~7112.7 eV of the Fe K-edge x-ray absorption spectrum of Fe(1.01)Se decreases for pressure from 0.5 GPa increased to 6.9 GPa. The satellite line Kβ' was reduced in intensity upon applying pressure and became absent for pressure 52 GPa. Fe(1.01)Se shows a small net magnetic moment of Fe(2+), likely arising from strong Fe-Fe spin fluctuations. The 1s3p-RXES spectra of Fe(1.01)Se at pressures 0.5, 6.9, and 52 GPa recorded at the Fe K-edge reveal that unoccupied Fe 3d states exhibit a delocalized character, stemming from hybridization of Fe 3d and 4p orbitals arising from a local distortion around the Fe atom in a tetrahedral site. Application of pressure causes suppression of this on-site Fe 3d-Fe 4p hybridization, and thereby decreases the intensity of the pre-edge feature in the Fe K-edge absorption spectrum of Fe(1.01)Se. Compression enhances spin fluctuations at Fe sites in Fe(1.01)Se and increases the corresponding T(c), through a competition between nearest-neighbor ferromagnetic and next-nearest-neighbor antiferromagnetic superexchange interactions. This result aids our understanding of the physics underlying iron-based superconductors.