My name is Yoshida Toshihide from the Soto sect. I will respond to the extent that I have seen and heard.
1. Even in the case of the Soto sect, I think there are many so-called hereditary temples. I was born in a temple in Iwate Prefecture. My older brother is the chief priest at my parents' temple. My biological father who passed away (born in Taisho 14) was not born in a temple. When I was in elementary school, I became a temple boy and became a monk. Until before the war, it seems that children were often given away at an early age to be feudal servants of merchant houses or monks in temples.
Even in the Soto sect, depending on the temple, there are temples where the son of the chief priest cannot be the successor. It is a temple that has a long history and is said to be prestigious. There are also cases where they are dispatched from Motoyama. Also, there are cases where they are selected from the temple's Hoshukai (related persons related to mentor/disciple) or selected from the branch temple association (branch temple group).
2. It is common to call the wife of the chief priest of a temple a temple family, a temple garden, or a monk. As a common name, they are also sometimes called “Okuri-san” or “Daikoku-san.” As already answered, shrine maiden (miko) generally refers to a female employee at a shrine.
Furthermore, historically, it seems that there are many cases where it is understood as a “shrine maiden = shaman.” In other words, a female religious person who performs acts such as “performing prayers and conveying oracles” or “possessing the spirits of ancestors and deceased people and making promises” is called a shrine maiden. In the fields of religious studies and folklore studies, in such cases, shrine maidens are called “fujo.”