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The potential for realizing the impacts of the left-right symmetric model(LRM) on the process e+e-→ μ+μ-at a possible Z0-factory is investigated.Under various electron-positron polarization collision modes, we calculate and compare the deviations of various observables in the framework of the LRM from the standard model(SM) predictions, such as the total cross section, the distribution of the transverse momentum of μ-, and the forward-backward charge asymmetry of μ-.In addition, we present the relations between the observables and the LRM parameters.We conclude that it is possible to observe the effects of the LRM on the process e+e-→ μ+μ-by using optimal observables and favorable parameters at a Z0-factory.We give the precision calculations for the e+e-→ q_ (q)_ processes up to the QCD next-to-leading order (NLO) including full weak decays for the fimal T-odd mirror quarks in the littlest Higgs model with T-parity (LHT) at the Compact Linear Collider (CLIC).We show the dependence of the leading order (LO) and NLO QCD corrected cross sections on the colliding energy √s, and provide the LO and QCD NLO kinematic distributions of final particles.The results show that the LO cross section can be enhanced by the NLO QCD correction and the (K)-factor increases obviously when the threshold of the on-shell q _ (q) _-pair production approaches the colliding energy √s.The K-factor value varies in the range of 1.10～ 1.39 in our chosen parameter space.We find that a simple approximation of multiplying the LO kinematic distribution with the integrated K-factor is not appropriate for precision study of the e+e-→ q_(q)_(q_(q)_ =u_(u)_, c_(c)_, d_d_, s_(s)_) processes, since the NLO QCD corrections are phase space dependent.It is necessary to calculate the differential cross sections including full NLO QCD corrections to get reliable results.