Lokesh - a top AEM Community member - addresses correct way to handle this use case here: Best practice to query JCR data using QueryBuilder API

Follow this end to end tutorial - the grid worked perfectly when I followed this one: Adobe Summit 2019 | L767 - Getting Started with Adobe Experience Manager Sites Development

I cannot find a good example on how to build a solution using AEM and magento.

Example here - Adobe Experience Manager Help | Creating Java Swing applications that posts files to AEM ClientLibs folders

The JavaDocs state its a valid API - FormData ("The Adobe AEM Quickstart and Web Application.")

As Jierg suggests, use a public facing API that AEM exposes.

Do you mean you want to code a Search component for your site?

Also - just so you know - the article that you referenced was for AEM Form that you create by using AEM Foundation components. If the form core component does not meet your needs - look at using the foundation form components.

No - this can only be done via manual.

Is it not submitting to post.POST.jsp?