Learn Polish: Myślę, że jego opinia o niej jest fałszywa. - I think that his opinion about her is false.

The preposition o (when it means 'about') requires the Locative case. The Locative form of ona (she) is niej. Notice how third-person pronouns often get an 'n' added to the beginning when they directly follow a preposition!

The word for 'his' is jego. Why doesn't it have a feminine ending to match the feminine noun opinia?

In Polish, the third-person possessive pronouns jego (his), jej (her), and ich (their) are frozen. They never change their endings to match the noun they describe, so jego stays exactly the same even next to the feminine noun opinia.

The verb myśleć (to think) often takes the preposition o. Why isn't it Myślę o at the beginning of the sentence?

When you want to say 'I am thinking about something', you use myśleć o + Locative. But here, you are introducing a completely new clause: 'I think that...'. For this, you use myśleć, że followed by a regular sentence, just like in English.

Why does the adjective at the end take the form fałszywa?