Learn German: Wir werden unser Eigenheim abbezahlt haben. Darüber freue ich mich. - We will have paid off our own home. I am happy about that.

It uses the conjugated verb werden in the second position, the past participle abbezahlt, and the auxiliary verb haben at the very end. This structure (werden + past participle + haben or sein) expresses that an action will be fully completed by a certain point in the future.

Why doesn't the past participle abbezahlt have a -ge- in the middle, like typical separable verbs?

The verb abbezahlen is made of the separable prefix ab- and the inseparable verb bezahlen. Because bezahlen starts with the unstressed, inseparable prefix be-, it never takes a -ge- in its past participle (bezahlt). When you add the separable prefix ab- to form the new word, it simply attaches to the front, giving us abbezahlt.

Since paying off the house is a future event, why does the speaker use darüber instead of darauf?

You usually use sich freuen auf (to look forward to) for future events and sich freuen über (to be happy about) for present or past events. However, by using darüber here, the speaker is expressing how they feel right now in the present about this guaranteed future achievement as a fact. If they specifically wanted to say they are looking forward to that day, they would use darauf.