Is the "adult" page a regular file in /ministries subdirectory or is /ministries a controler with 'adult' a value of page parameter (like a :page_id, or :slug etc.)? Have a look at this piece of documentation, it might be helpful https://octobercms.com/docs/markup/filter-page, see the diference between links to pages in subdirectories and links to generated pages via Reverse routing.
Just read documentation about Plugins: https://octobercms.com/docs/plugin/registration
It's really short and after one day you will have your first plugin working.
You can also take a look at my Reservations plugin https://github.com/vojtasvoboda/oc-reservations-plugin It contains a component with frontend form which fills data to backend as you wanted.