What is the ruling on medicines and nutritional supplements derived from animal sources that have not been ritually slaughtered (ghayr madhkah), such as vitamins, fats, and amino acids, and do these substances fall under the ruling of transformation (istihalah)?

The food product mentioned is plant-based, and the default ruling for it is permissibility. As for products containing animal fats, if they are from a carcass or an animal unlawful to eat (like pork), and their processing has transformed them into another substance, then they are pure and permissible to use. If they have not transformed, they remain impure and unlawful. As for products whose status and source are unknown, the default ruling for them is permissibility due to the widespread difficulty and the unknown origin, and they have often been processed and transformed from their original state. One can inquire with the manufacturer to ascertain this.