Regarding question #3: the order is up to you. In my opinion, DMV is the lowest priority. I've applied first for a U.S. passport & passport card.
Updating the SSA is currently somewhat tricky, as their offices are closed, and in order to update your citizenship status, they ask you to send an original document that proves citizenship (U.S. passport of naturalization certificate). From this and other forum members, it seems that SSA sometimes loses those documents. I'll wait until SSA reopens and update my status in person, as there's no rush with that, too.
As long as SSA is not updated, you might not be able to register online to vote. That's also not a problem, as you can register to vote in person at your county's recorder's office, town clerk's office, etc. with your U.S. passport or naturalization certificate.
Congratulations on becoming a U.S. citizen!