Newbie Random NFA DFA questions
Answers to your questions in given order: (a) Yes, an NFA could in principle be converted into multiple distinct DFAs for the same language.  Note however: There is always a unique DFA having a minimum number of states; other DFAs would have to be 'redundant' in some sense.  (b) There may be different methods, though I am only aware of one.  As long as the resulting DFA recognizes the same language, I would say the conversion method would be considered correct.  (c) No, the expression d(q0,e,q2) would NOT be correct; however for every transition function $d$ there is a corresponding transitive closure $d^*$ for which that would be a valid expression.  (d) No, it is not correct to assume the existence of 'hidden' e transitions; all defined transitions, e or not, must be given explicitly, but it is permissible to leave some transitions undefined (and any NFA-to-DFA converter must handle that case).  (e) Not only is it NOT 'bad practice' to have multiple NFA states as one DFA state, that is the standard tactic used by the canonical NFA-to-DFA procedure.