The Requesting Help topic contains useful tips about learning Hugo. Please read it.
However also note that your questions are more complex than you may realise.
It is not trivial to connect a payment gateway with a static site without doing it server side.
This forum is not meant for general web development questions.
Please try searching other channels to find answers to your questions regarding adding payment processing to websites. Also the payment gateway you want to use should provide documentation for developers who want to use it.
Regarding the Vex theme you basically need to override the templates -partials etc.- that contain the code for the Snipcart checkout UI with what you wish.
To override a template you need to replicate its directory PATH under the root of your project.
For example /themes/vex-hugo/layouts/partials/footer.html can be overriden at
/<your-project-directory>/layouts/partials/footer.html
This topic is kind of OT so I am closing it.
Thank you for the understanding.