Voting is a privilege reserved to citizens. Folks who naturalize often are very interested in taking advantage of that privilege an signing up to vote.
In Texas, you register to vote by county. You fill in an application to get a "voter registration card" and mail to to a county official. You can vote 30 days after you are registered to vote. There are local elections in early May in many municipalities in the Dallas area, so, if your oath ceremony is more than 30 days before that date, it might be worth rushing to get registered. If you can't make the early May elections, then there is no rush.
You can get the applications on the web, at your local city hall, or at the oath ceremony. They cost nothing to mail (well, the web-based one requires a stamp). The easiest way to register is to get the application immediately after the ceremony (you need to know what county you live in), fill it out and mail it on the way out. No fuss, no bother.
The social security thing is simply that there are differences in the social security rules for citizens and non-citizens (no, I don't know what they are). So, the Social Security Administration wants to know if you change your status.
We simply went to the SSA office on rt 360 in Grand Prairie and waited until our number was called. We showed our natz certs (and my daughter's new US Passport) and our social security cards. The clerk typed away and said we were all done. Neither my wife nor I got new cards. My daughter still had a "not valid for employment without authorization" note on here card. So, they shredded that card and a new one showed up in the mail a week or two later (same number).
I don't think that there is any rush for the SSA thing - though I'm guessing should do it the same tax year as you when you naturalize. In our case, we did it 1 month after my naturalization and nearly 6 months after my wife's (and about a month before the end of the year).
For your ticket, consider going to city hall or the clerk of whatever authority it was that issued your ticket, paying off the ticket in cash and taking the receipt to your oath ceremony.