Since no official documentation is available for Magento API 1.x, Where do you recommend I look for information on how to integrate my web app to a Magento shop running 1.x?
Thanks.
You can find few articles here:
http://39.108.91.212/guides/m1x/api/rest-api-index.html
https://www.eglobeits.com/blog/how-to-access-magento-rest-and-oauth-settings-for-rest-api/
It can help for sure.