A princess is a woman in a royal family who may be a daughter, wife, or ruler, a small-country leader with monarch power.

A princess is a word used for some women in royal families. She can be the daughter of a king or queen, the wife of a prince, or the ruler herself.
A crown princess is a special kind of princess who may be the next ruler-to-be or the wife of the next ruler.
A princess regnant is a princess with real ruling power. There have been fewer ruling princesses than ruling princes because in the past many places did not let women inherit the throne.
A courtesy title is a name people use for a royal person even when it does not mean they rule. Daughters of a king or queen in Britain were sometimes called "Lady" long ago, and over time more family members received the title princess as a courtesy.
Long ago, daughters of a king or queen were not always called princesses and might be called Lady. Over time, more daughters and other close family members received the title princess as a courtesy to show their place in the royal family.
Yes. Many wives of princes are called princesses as a courtesy, to show their connection to a prince rather than that they rule.