Learn Turkish: Onun hikâyesine inanıyoruz.

You spotted them! The root word is hikâye (story). First, we add the 3rd person possessive suffix to make it 'his story'. Since hikâye ends in a vowel, we use the buffer -s- to get hikâyesi. Next, we need to add the dative case suffix -e. When adding any case suffix right after a 3rd person possessive suffix, Turkish requires the buffer letter -n-. So, the final word is hikâye + -si + -n- + -e.

Why does the sentence use the dative ending -e on the story when the English translation says 'believe in'?

In English we 'believe in' things, but in Turkish, the verb inanmak (to believe) always takes the dative case, which usually means 'to' or 'towards'. You can think of it as directing your belief to his story. This is why we use the dative -e instead of the locative case (-de or -da for 'in').

Could we just say Hikâyesine inanıyoruz without the word onun?

Yes, absolutely! The possessive suffix -si in hikâyesi already tells us it means 'his', 'her', or 'its' story. Including the pronoun onun just adds a bit of emphasis, like saying, 'We believe his story (but maybe not someone else's).'

Why do we use the present continuous tense (inanıyoruz) for 'we believe'? Doesn't that mean 'we are believing'?