What happens during the DFA reversal construction if the initial state is final? The steps in reversal of DFA are :-


Make final state as initial state. If there are more than 1 final state, then make a new start state with epsilon transitions to these states.
Change all initial states to final states
Reverse the direction of edges.


Now what if I have a state which is both initial and final ? Will it be initial or final state in the reversed dfa?
Yes.  It will be both initial and final in the reversed automaton.

(Separately: If you want the reversed automaton to be a DFA, you may have to be a bit careful about your construction for reversing a DFA, as DFAs are not allowed to contain epsilon transitions.)