Hi Dave,
Thank you for the details, it helps us a lot.
1. I’m assuming, that the product code is not part of the content, but it might be a custom field, like the product SKU, which might not be selected for search. On the General Options -> Sources panel, try enabling the search for the ‘_sku’ custom field, that might do the trick: https://i.imgur.com/xcG1mgR.png
2. You have a grouping by post type or categories(?) enabled, if I see correctly. Since that post type or the product catgories taxonomy, where the product belongs to is not selected under the grouping options – it is automatically moved to the “other results” group, which is generally on the bottom of the list. Make sure that the product_cat is also selected when using the category based gouping: https://i.imgur.com/UNMQZiK.png
You can also enable this option, so that the groups are re-ordered by the most relevant results: https://i.imgur.com/yYK5dyC.png
