You can look online to see if your client is still incarcerated before you head out there. You do not need an appointment. You cannot take your cell phone in. Depending on who is at the desk that day, you’ll need your bar card (usually they just ask me the number), and your TDL. I also take my Travis Co attorney badge to hasten the process.
Thanks to the new ‘declaration’ language that negates the need for a notary on the affidavit of indigence and some other documents, you won’t need a notary for those. For a relinquishment, a notary is often on staff. You just need to ask them what their preferred procedure is. I’ve only done it twice there over 4 years, but both times I notified the notary up front, had two staff in the back witness my client sign, add their signatures, and then take that completed form with the three signatures up to notary. Again, it’s notary specific so please check but at least you can have peace of mind that it’s possible to get these types documents executed even though your client is incarcerated.