Hello there
I have gone through your project description carefully. I have worked in multiple projects in android, accessing wifi and wifi-hotspot (with and without reflection approach). Integrating the paytm gateway is pretty straight forward.
For the laptop/pi side, you haven't mentioned what platform I should be using. Anyway, I am comfortable to work with java and python. I can build you a nice system app, which will listen for incoming connections on a http port and take action(Database entry and file copying) according to that.
For the QR part, I think it's better the system app generate the QR code dynamically, which will expire after a fixed time. This will give an added layer of security to the system, as I think it's a bad idea to use static QR code for this purpose.
Anyway, Let me know if you are interested.
Thanks