Learn German: Werden wir dieselbe Geschichte hören?

The word for 'the same' changes to match the gender and case of the noun it describes. Here, it describes Geschichte (story), which is a feminine noun (die Geschichte). Because the story is the direct object being heard, it is in the accusative case. The feminine accusative form is dieselbe. Notice how it is simply the definite article die attached to the word selbe!

Is there a difference between dieselbe Geschichte and die gleiche Geschichte?

Yes, and this is a classic German distinction! dieselbe means the exact identical thing, meaning one specific story being told again. die gleiche means two things of the same type or exactly alike, such as two people telling similar stories independently. Since they are asking if they will hear that one specific story again, dieselbe is the best fit.

Why is the main verb hören all the way at the end of the sentence?

This sentence is asking a question in the future tense. The future tense is built using a conjugated form of the helping verb werden (here, werden to match wir) and the dictionary form (infinitive) of the main verb (hören). In German, helping verbs always push the main infinitive verb to the very end of the clause.

How would we say 'Will we hear the same one?' without repeating the word Geschichte?