Dielectronic recombination (DR) plays an important role in understanding atomic processes and identifying spectra, including astrophysical and tokamak plasmas in particular. Because this process involves numerous singly- and doubly-excited autoionizing states, which merge with continuum states, it is challenging to calculate, and relativistic data for a lot of ions do not exist. This paper focuses on relativistic calculations of dielectronic recombination in Ar-like Ni and dielectronic satellite lines in K-like Ni. Specifically, energy levels, radiative transition probabilities and autoionization rates for the [Ne]3s23p53dnl (n = 4-7), [Ne]3s23p54l'nl (n = 4-7), [Ne]3s3p63dnl (n = 4-7), [Ne]3s3p64l'nl (n = 4-7), [Ne]3s23p55l'5l and [Ne]3s3p65l'5l states in K-like nickel (Ni9 +) are calculated by the Hartree-Fock relativistic method (Cowan code) and the relativistic many-body perturbation theory method (RMBPT code). In addition, these results are compared with atomic data from two more codes, HULLAC and FAC, as well as with the NIST data. DR rate coefficients are determined for the singly-excited [Ne]3s23p6nl,(n = 4-7), as well as non-autoionizing doubly-excited [Ne]3s23p53d2, [Ne]3s23p53d4l, [Ne]3s3p63d4s and [Ne]3s3p63d4p states. Contributions from the autoionizing doubly-excited states [Ne]3s23p53dnl and [Ne]3s3p63dnl (with n up to 500), which are very important for calculating total DR rates, are estimated. Synthetic dielectronic satellite spectra from K-shell Ni are simulated in a broad spectral range from 45 to 600 Å.