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Any dfa which accepts epsilon will have initial state as final state.

Coming to the second part of your doubt: More than 1 final states and initial state as final state. So suppose

L= a language over {a,b}

L= atmost 2 a's={epsilon,a,aa,ab,ba,aba,.......}=b*+b*ab*+b*ab*ab*

So we have more than one final states here and initial state is also final.

So see the following dfa:

For further ref:https://www.cs.odu.edu/~toida/nerzic/390teched/regular/fa/min-fa.html

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