Particle-Antiparticle Mixing, epsilon_K, Delta Gamma_q, A_SL^q, A_CP(B_d -> psi K_S), A_CP(B_s -> psi phi) and B -> X_{s,d} gamma in the Littlest Higgs Model with T-Parity

We calculate a number of observables related to particle-antiparticle mixing in the Littlest Higgs model with T-parity (LHT). The resulting effective Hamiltonian for Delta F=2 transitions agrees with the one of Hubisz et al., but our phenomenological analysis goes far beyond the one of these authors. In particular, we point out that the presence of mirror fermions with new flavour and CP-violating interactions allows to remove the possible Standard Model (SM) discrepancy between the CP asymmetry S_{psi K_S} and large values of |V_ub| and to obtain for the mass difference Delta M_s X_s gamma decay and A_CP(B -> X_s gamma) that are presented in the LHT model here for the first time. In another scenario the second, non-SM, value for the angle gamma=-(109+-6) from tree level decays can be made consistent with all existing data with the help of mirror fermions. We present a number of correlations between the observables in question and study the implications of our results for the mass spectrum and the weak mixing matrix of mirror fermions. In the most interesting scenarios, the latter one turns out to have a hierarchical structure that differs significantly from the CKM one