Is “之” usually used as a possessive pronoun (attributive) in Classical Chinese?
之 is a common way to say ‘him/her/it’ in classical Chinese.  It’s usually in the object position, not the subject one though:  殺之 ‘kills him’;   由之  ‘from it’.  The use like modern Chinese 的 is different.

其 is actually a possessive pronoun, as in 其妻  ‘his wife’.  More generally, it substitutes for ‘noun + 之’.

彼 can be used as a third-person pronoun in either subject or object position, but mainly it is a demonstrative (‘this’ or ‘that’).  There are other words that work the same way and appear as pronouns.

All of this is based on the section on pronouns in Edward Pulleyblank’s ‘Outline of Classical Chinese’, esp. pp 79-80.  You can find it on Google Books.