Short answers, pulled from the story.
Kashrut is a set of dietary laws dealing with the foods that Jewish people are permitted to eat and how those foods must be prepared according to Jewish religious law. The term comes from the Ashkenazi pronunciation of the Hebrew word meaning fit, while the Sephardi or Modern Hebrew pronunciation is kashér. Food that may be consumed is deemed kosher, whereas food that may not be consumed is deemed treif.
Mammals that both chew their cud and have cloven hooves can be kosher, but animals with one characteristic but not the other are specifically excluded. The camel, the hyrax, and the hare are excluded because they have no cloven hooves, and the pig is excluded because it does not ruminate. In 2008, a rabbinical ruling determined that giraffes and their milk are eligible to be considered kosher, as the giraffe has both split hooves and chews its cud.
The most basic eating rule in the Torah is that blood is not to be consumed, and this prohibition drives the entire process of ritual slaughter known as shechita. A certified ritual slaughterer, called a shochet, must sever the trachea, esophagus, carotid arteries, and jugular veins in a single, quick cut using an ultra-sharp instrument called a chalaf. This process causes rapid and massive blood loss, ensuring the animal dies instantly without unnecessary suffering.
According to David C. Kraemer, the practice of keeping separate sets of dishes developed only in the late 14th and 15th centuries. Before that time, it was possible that observant Jews waited overnight for the meat or dairy gravy absorbed in a pot's walls to become insignificant before using the pot for the other foodstuff. The Shulchan Aruch, a code of Jewish law, recommends a six-hour waiting period, during which it is generally advised to abstain from brushing and rinsing the mouth.
Fish must have fins and scales to be kosher, and shellfish and other non-fish water fauna are not kosher. The only exception to the rule regarding invertebrates is locusts, which are the only kosher invertebrate, though most communities lack a clear tradition regarding which specific species of locusts are permitted today. Insects are not kosher, except for certain species of locust or grasshopper that, according to most, cannot be identified today.
This flexible practice emerged in the 1920s amongst Jews assimilating into American society, who sought connection to their heritage without fully observing dietary laws. Hasia Diner, a professor of American Jewish history at New York University, suggests that kosher style represents a balancing act between tradition and assimilation, providing a sense of Jewish identity through food without strict adherence to kashrut. The term is broad and encompasses foods that could be kosher, like chicken noodle soup or pareve meals, even if they don't meet halakhic standards.