Finales:
Finales are a specific subset of Rotes tied to a specific Martial Style and philosophically something of the 'end point' of that Style, and they are used to end fights, hence the name. Unlike most Rotes, they cost Zeal to use, in significant quantities, and can usually only be countered by other Finales or effects on a similar level from monsters or the environment, or occasionally a particularly clever plan involving the Finale's specific limitations.
Because most Finales have limitations of one sort or another. This is because it grants them power, and when two applicable Finales clash, it is the one with more severe limitations that almost universally emerges triumphant. This makes Finales without any restrictions rare.
Exactly what Finales do and what limitations they are under vary by the Finale, but generally speaking they are an attack that will defeat, and almost universally kill, one or more opponents (whether they hit multiple people varies by the Finale), but occasionally a defense designed to stop other Finales also qualifies, particularly if it involves a counterattack.
Learning Finales mostly works like learning any other Prayer, but you must actually use them to train them past the very basics, which costs Zeal. Specifically, you must actually perform the Finale at least once in order to get it to Refined, and then use it in battle at least a few times to get it to Mastered, and use it in battle quite a bit to get it to Perfected.
Technically, the 'first use' needed to get it to Refined could also be done in battle, but given the possibility of a Rough Finale backfiring or failing at a critical moment, this is not recommended. Learning multiple Finales for the same Martial Style also becomes harder, as your philosophy on the Style needs to change and evolve for that. There are no rules penalties for learning a second Finale in a single Style, but the third and subsequent ones will become more mechanically difficult.
Finales, as mentioned, cost Zeal to use rather than Fervour. They all have a flat Zeal cost and then add the wielder's Decade x 3 in additional Zeal as well. Technically, you can use less, down to a minimum of Base Cost + 3 for a 'First Decade' level Finale, but powering down your Finale can easily result in it failing, which is almost universally bad, especially versus opponents you think are worth using a Finale on. Their costs do not change with level of mastery, with them instead doing increasingly better in contests with other Finales.
Audrey is aware of several possible Finales in her own Martial Styles, but they are far from the only options available. Most warriors who use more than one or two Finales eventually wind up inventing at least one personally.