as far as State law, it is governed by chapter 46 of the Texas Penal code. With out going into all the giberish lawyer talk of the section, it basicly comes down to these points:
Don't transfer to anyone under 18 yoa(exceptions available for your child)
don't transfer to a known felon
don't knowingly transfer to someone under a protective order
don't transfer to an intoxicated person
don't transfer to someone you know is pi**ed and about to commit a crime
There is nothing in State law that i am aware of that says you must obtain the ID of the buyer for your records or prohibits you from a "private treaty" transfer of a weapon anywhere, including a show. But i believe it is in your best interests to obtain a bill of sale with ID info if you are buying or selling in any weapon transfer just to cover yourself liability wise.
As far as i know there is nothing in the federal regs about such either but i mainly am concerned about State law. I'm familar with a few federal regs and they purty much follow our State law. They also mention speciically do not transfer an handgun to the resident of a different State other than your own. There are a few others that i can't remember and if it ain't State law, i just let the ATF boys worry about it.
Now as far as city regulations, i just don't know. Some municipalities may have ordinances governing such on city/county property at a gun show----but i'm not aware of them but its possible.