This dissertation presents measurements of charge-particle distributions as well as searches for Supersymmetry in top-quark-pair final states with the ATLAS experiment at the LHC. The measurements of charged-particle distributions use data from pp collisions at a centre of mass energy of 13 TeV and select charged-particles with transverse momenta above 100 MeV. They are sensitive to non-perturbative QCD effects. The observed data are corrected and unfolded in order to take any detector effects into account. The charged-particle distributions are compared between the observed data and the prediction from different, QCD inspired models. The result of the measurements can be used to improve the overall prediction for Monte Carlo generators and thus is an input for further precision measurements and searches. The searches in top-quark-pair final states with additional missing transverse energy use pp collision data corresponding to 36.1/fb-1 at a centre of mass energy of 13 TeV. Two dedicated analyses are presented, targeting different mass regions in models of light top squarks. Both analyses rely on shape fit techniques in order to maximise the sensitivity to the signal models. The dominant backgrounds are normalised and the modelling is validated in dedicated regions. No excess is observed, and exclusion limits on models of Supersymmetry are set. The sensitivity of previous searches is extended by both analyses, excluding previously unconstrained regions in the model parameter space. Top squark masses between 198 GeV and 460 GeV are excluded for the compressed region, where the mass difference between the top squark and the neutralino is approximately the top quark mass. For neutralino masses below 300 Gev, top squark masses up to 980 GeV are excluded.