1) Yes, the NEB methodology can find the energy barrier for any process that is contingent on one or more atoms moving in a constrained way from one stable state to another. It is usually the method of choice for finding energy barriers during chemical reactions. For more details, I suggest you consult the original references.
1) + 2) In general, simple energy considerations work well, but usually it is also necessary to include other contributions to the free energy. For more information, I will suggest you study the work of e.g. H. Jonsson, J. K. Nørskov, K. Reuter, M. Neurock and others.