It would be really helpful, if you were able to formulate your questions in a comprehensive manner and your statements in a non-tautological and non-repetitve way.
A perturbation (of a system found in an equilibrium state) is simply a (generally) small interaction to which the object(s) under observation is(are) subject to.
In a quantum mechanical setting, a perturbation is described by a new term added to a Hamiltonian operator whose spectral problem is completely solved.