Normalised multi-differential cross sections for top quark pair ( (\text{t}\overline{\text{t}}) ) production are measured in proton-proton collisions at a centre-of-mass energy of 13 (\phantom{\rule{0.166667em}{0ex}}\text{TeV}) using events containing two oppositely charged leptons. The analysed data were recorded with the CMS detector in 2016 and correspond to an integrated luminosity of (35.9\phantom{\rule{0.166667em}{0ex}}{\text{fb}}^{-1}). The double-differential (\text{t}\overline{\text{t}}) cross section is measured as a function of the kinematic properties of the top quark and of the (\text{t}\overline{\text{t}}) system at parton level in the full phase space. A triple-differential measurement is performed as a function of the invariant mass and rapidity of the (\text{t}\overline{\text{t}}) system and the multiplicity of additional jets at particle level. The data are compared to predictions of Monte Carlo event generators that complement next-to-leading-order (NLO) quantum chromodynamics (QCD) calculations with parton showers. Together with a fixed-order NLO QCD calculation, the triple-differential measurement is used to extract values of the strong coupling strength ({\alpha }{S}) and the top quark pole mass ( ({m}{\text{t}}^{\text{pole}}) ) using several sets of parton distribution functions (PDFs). The measurement of ({m}{\text{t}}^{\text{pole}}) exploits the sensitivity of the (\text{t}\overline{\text{t}}) invariant mass distribution to ({m}{\text{t}}^{\text{pole}}) near the production threshold. Furthermore, a simultaneous fit of the PDFs, ({\alpha }{S}), and ({m}{\text{t}}^{\text{pole}}) is performed at NLO, demonstrating that the new data have significant impact on the gluon PDF, and at the same time allow an accurate determination of ({\alpha }{S}) and ({m}{\text{t}}^{\text{pole}}). The values ({\alpha }{S}\left({m}{\text{Z}}\right)=0.1135{}{-0.0017}^{+0.0021}) and ({m}{\text{t}}^{\text{pole}}=170.5±0.8\phantom{\rule{0.166667em}{0ex}}\text{GeV}) are extracted, which account for experimental and theoretical uncertainties, the latter being estimated from NLO scale variations. Possible effects from Coulomb and soft-gluon resummation near the (\text{t}\overline{\text{t}}) production threshold are neglected in these parameter extractions. A rough estimate of these effects indicates an expected correction of ({m}{\text{t}}^{\text{pole}}) of the order of (+1\phantom{\rule{0.166667em}{0ex}}\text{GeV}), which can be regarded as additional theoretical uncertainty in the current ({m}{\text{t}}^{\text{pole}}) extraction.