In polite speech, it is customary to refer to one’s own things or actions in the humble form, and to refer to others (especially people who should be treated with respect, such as customers) in the honorific form.

When you say, “I do something (for you)”, since the subject is “I”, it is your action, and you refer to your action using the humble form:

On the other hand, you refer to someone else’s (such as a customer’s) action using the honorific form:

These forms are typically used when one is required to speak very politely, such as when speaking to customers. However, overly polite speech can lose its sense of “closeness” or “friendliness,” so some people use more casual language with customers. These forms are mainly used to add a nuance of politeness to speech.

居酒屋いざかや literally means "staying liquor shop". It originally refers to a liquor shop that also served food. Customers who came to buy sake, sometimes taste it on the spot, and shopkeepers started offering some food to keep them around. Over time, this “staying and drinking at the sake shop” practice became institutionalized, giving rise to the word 居酒屋いざかや.

Today, an izakaya is no longer a liquor shop that sells bottles, but a dining establishment that serves both alcohol and dishes to accompany it. While the main focus of an izakaya is still the alcohol, it differs from what is called a “bar” in the West in that it offers a wide variety of food. Local specialties can also be enjoyed, and these days, many people who don’t drink alcohol visit izakaya simply to enjoy the food.

Izakaya come in different styles. Some are chain establishments that can accommodate over a hundred customers, while others are tiny, like a shop run by a grandmother with only eight seats. Many people prefer these small-scale izakaya because they create a homely atmosphere, where customers can chat with the owner and enjoy the owner’s homemade cooking.

Here are pictures of some food mentioned in the dialogues.

焼やき鳥とり literally means “grilled bird” and originally referred to chicken cooked on skewers, usually over a charcoal fire. Nowadays, the term yakitori is used more broadly, it generally refers to the traditional Japanese style of cooking meats and vegetables on sticks. In this sense, it’s used as a general term for this cooking method, not necessarily limited to chicken.