Texas requires a photo ID to vote. Not sure about the other two states.
Not really.
Under Texas law, voters who possess one of the seven acceptable forms of photo ID must present that ID at the polls when voting in person. Voters who do not possess and cannot reasonably obtain one of the seven approved forms of photo ID may fill out a Reasonable Impediment Declaration (RID) (PDF) at the polls and present an alternative form of ID, such as a utility bill, bank statement, government check, or a voter registration certificate.The second part completely undermines the requirement. "You have to show a government photo ID, unless you can't."
(https://www.votetexas.gov/mobile/id-faqs.htm)
I have never tried to mail in a vote. Texas does require an actual unexpired ID to vote in person.
Pennsylvania requires photo ID for first time voters; Arizona requires photo ID.