Can every state in a DFA be an accepting state?
Yes, every state can be accepting.  Assuming the transition function is total (complete), so every state has a transition out on every possible letter in the alphabet, then yes, this would recognize all strings in the DFA's alphabet: the DFA would recognize $\Sigma^*$.

If the transition function is not complete -- in other words, if there is some state $q$ and some letter $a$ where there is no transition out of $q$ on letter $a$ -- then the DFA doesn't necessarily recognize all of $\Sigma^*$.

See In a DFA, does every state have a transition on every symbol of the alphabet? for more on that distinction.  To avoid confusion, I generally recommend sticking to DFAs whose transition function is complete (total), at least until you understand the concepts well.