In Sons and Daughters (1997), Worf tells Jadzia that she must, "present [her] d'k tahg to General Martok as a formal request for him to accept you into our House" during the wedding ceremony. Here, Jadzia requires the approval of Martok's wife, Sirella, to join the House before the wedding can take place.
When Sirella and Jadzia converse, they speak mostly in English but sometimes swap into Klingonese. Since it can be assumed that Sirella, a Klingon traditionalist, would not actually be speaking another language, then all the English dialogue heard must be translated for both Jadzia's benefit and the audience's (mostly the audience, since Jadzia is fluent in Klingonese). That being the case, there's no reason for some dialogue to be translated and some not.
Alexander relates a story in which he accidentally flooded an entire deck of the Rotarran with "superheated fluid," with the source of amusement coming from how long it took to clean up. Superheated fluid is compressed fluid that is well above its normal boiling point (for water, above 100 °C (212 °F) and as high as 374 °C (705 °F)). If a deck were flooded with such fluid, it would do considerable damage to the area, as well as any crew that happened to be nearby. It would also likely evaporate quickly once released from its pressurized storage, which could create its own problems. Cleanup would not be the issue, danger to equipment and life would.
Worf tells Alexander that he would like for him to be his Tawi'Yan (sword-bearer, a Klingon equivalent of a best man). Alexander, not a native speaker of Klingonese, needs Jadzia to translate the term for him. All of them, however, are equipped with universal translators (Alexander likely relying on his to serve aboard a Klingon ship without speaking the language). There is no reason the universal translator wouldn't translate this term for Alexander.
Based on what is known of Klingon culture, it seems unlikely that Jadzia begging for Sirella's forgiveness would curry her favor. Klingons would view that as weakness. Besting another person in combat, however, as Jadzia does to Sirella, is seen as a show of strength and would be looked upon favorably.
While reciting the history of the women in Sirella's family, Jadzia reveals that her research uncovered that Sirella's 26th maternal grandmother was not, in fact, a member of the traditional imperial family, but rather a concubine who was recruited to portray a member of the royal family after the originals had been killed in an uprising. That being the case, Sirella wouldn't have actually been related to any of the people Jadzia had already recited the history of.
Worf and Jadzia move up their wedding plans so that they can have their wedding before Alexander is reassigned at the end of the week. Jadzia is afraid Alexander might miss the ceremony due to his service in the Klingon militia otherwise. But Worf clearly states that they had agreed to hold the ceremony on Qo'noS after the war ends. Once the war ends, the Klingon militia will not be in so desperate a need of soldiers and Alexander will likely be allowed leave to attend his father's wedding. Jadzia's thoughts on the matter only make sense if she and Worf were planning on holding the wedding during wartime, but that is not the case.