Yes, if have a programmable TI calculator, such as the TI-84, and most of the higher ones from that point.
If you do want to text message, then you need a calculator-to-calculator cable, and a program on both that allows texting. Of course, because the calculator cable is only about a foot long, it would be slightly redundant to be texting unless instead of talking. For an examples of such a program, try this page: http://www.ticalc.org/pub/83plus/basic/programs/linking/
However, you can't actually text wirelessly.
Chat with our AI personalities
Yes, but its rather pointless. The two calculators have to be linked via a link cable, and both need to be running the same chat client. Furthermore, since most chat clients utilize the Get( and Send( commands in TiBasic, there are for the most part slow. Rather than trying to communicate via a calculator with someone who is inches away from you, why don't you try a) face-to-face communication, b) passing a note, or c) sms texting?
I do recall that Brandon Wilson successfully modded a calculator for Bluetooth connectivity, but that is more than likely impossible for you to do anyways.