Is it possible for a DFA to have one state with an empty alphabet?

Question

I am confused if this is a valid DFA or not.

Answer 1

Yes. That one state must be the initial state. If it is also an acceptor state, the DFA accepts the language $\{\epsilon\}$; if not, the DFA accepts the language $\varnothing$. Both of these are languages over any alphabet, including the empty alphabet.