i doubt its your airbag module. have someone with vag com scan it. most likely you put to much tension on the connector harness on one of your seats. simply fix would be a resistor to the pin of the harness plug. usually on the bottom of the seat or in your glove box. once resistored have a vag-com delete the airbag code.
for your ESP light heres a link wih small detail about the lights and system, seems like a steering angle sensor
The Audi TT Forum :: View topic - esp & abs light
audi certainly arent the best cars to own out of warranty, however if you enjoy it i would recommend getting a vag-com tool. very useful and costs the same as a diagnostic, but you can use it again and again to save money in future.