Accurate excitation parameters are required to interpret the ultraviolet and X-ray spectra of Fe^13+^. In this work, we use the autostructure code to describe the atomic structure of Fe^13+^. The 197 lowest-lying fine-structure levels of the 3s^x^3p^y^3d^z^(x+y+z=3), 3s^2^4l, and 3s3p4{s,p, and d} configurations are included along with further correlation configurations: 3s3p4f, 3p^x^3d^y^4l (x+y=2), 3l4l'4l", and 3l3l'5l". The resultant level energies, lifetimes of excited states, and oscillator strengths of transitions between these levels are assessed by comparison with available experimental data and previous calculations. Electron-impact excitation data among these lowest-lying levels are generated using the intermediate-coupling frame transformation R-matrix method. We assess the present results by comparisons with laboratory measurement for the excitation to the metastable level 3s^2^3p^2^P^o^_3/2_ and with available close-coupling calculations for other excitations. Using these data and a collisional-radiative model, we have analyzed soft X-ray and extreme-ultraviolet spectra from space satellite observations of a stellar corona and of solar flares, as well as measurements from an electron beam ion trap. We assess the contribution from Fe^13+^ emission lines in the solar and Procyon corona observations, and find and identify new lines in the X-ray region observed in the solar and Procyon coronae. The laboratory measurements also confirm that weak lines (218.177{AA} and 224.354{AA}) of Fe^13+^ contribute to the observed intensities in solar observations. The polarization effect due to the directional monoenergetic distribution of the electron energy has been taken into account in comparison with the laboratory measurements. Electron density diagnostics for the astrophysical plasma sources have been performed using the updated data so as to investigate their sensitivity to the atomic data source.