If I can add few words,
자신있다 can be used when describing a person/subject of their/its state of being confident. (e.g. I'm/You're/She's/He's confident)
(만만있다 is an incorrect expression but it can be used as 자신만만하다 as an idiom. It also describes a state of being confident. A difference between 자신있다 with this idiom is that 자신만만하다 conveys meaning like "super confident.")
*caveat: 만만하다 without 자신 carries a totally different meaning, and often observed in a picking-up-a-fight or sarcastic line.
당당하다 has two usages. One is the same usage as 자신있다 but more frequently is used when describing the state of being 'not' guilty when he/she should have been. For example, "He committed the crime but he didn't apologize to victim's family nor said he was guilty on the court today. He has no shame." You can say, "오늘 법정에서 그는 범죄를 저질럿음에도 불구하고 피해자 가족들에게 사과하기는 커녕 죄를 인정하지도 않았다. 그는 정말 당당하다."
떳떳하다 has the same usage as 당당하다 and can be replaced in a place of 당당하다, except that it doesn't have the meaning of describing the state of being confident like 자신있다 / 자신만만하다.
확신하다 means closer to "sure." So, if you ask "are you sure?" then it's truer to a translation of "너 확실해?" than "너 자신있어?" 너 자신있어? would be translated into "Are you confident?"
자부심 is a self-esteem or pride on something that one has a certain type of relations/association with. It's similar to 자신감, but has a subtle nuance in 자신감 being proud of one's self. For example, if he/she has a lot of pride in his/her invention, one can say 그/그녀는 그/그녀의 발명품에 대한 자부심이 강하다. If he/she has a lot of pride on his/herself, it can then be translated into 그/그녀는 자신에 대한 자신감이 강하다/많다. So it is possible to have a lot of 자부심 on something but low 자신감 on one's self.