Kintsukuroi is the art of repairing pottery with gold (or silver) lacquer, and about the understanding that the piece is more beautiful for having been broken. It literally means "to repair with gold".
Otsukaresama desu is a really common expression in Japan. Even though it sounds weird in English, it literally translates as “honorable tired person".
It is often used to thank people for their efforts, actually meaning something like “thanks for working hard". It is commonly used after work for co-workers and in sports towards teammates after an event or practice.
Kanpai is the word the Japanese use at toasts, kind of equivalent to "cheers". It's often used in celebratory settings and at the start of meals and drinks with friends and/or guests.
The translation is literally "dry glass".
行灯 (andon) is the name of that traditional Japanese lamp made of stretched paper over a frame of bamboo (other types of wood and even metal are used as well, but it's not as common) in a rectangular shape.
So 「昼行灯」(hiru andon, "daytime lamp") is an expression used to describe something or someone that seems to have no purpose.
「いたいのいたいのとんでいけ!」 - Itai no itai no tonde ike!
A cute expression used to kiss a boo-boo away. The translation would be something like "Pain, pain, go away!".