Does the hadith about the Qur'an being revealed on the twenty-fourth of Ramadan, which Al-Albani graded as hasan, mean that Laylat al-Qadr is the twenty-fifth night of Ramadan? And do gatherings conclude with salutations as reported from the Prophet, peace and blessings be upon him?

The hadith referred to in the question was graded as hasan (good) by Al-Albani. The descent of the Qur'an mentioned occurred on the twenty-fifth night, all at once, to the lower heaven. Thereafter, it descended gradually according to events and occurrences. The utmost that can be concluded from this is that the descent took place on the twenty-fifth night, and that this coincided with Laylat al-Qadr in that specific year. It does not imply that it is fixed on the twenty-fifth, but rather that it moves among the odd nights of the last ten nights of Ramadan.

As for concluding the gathering, it should be with the supplication: "Glorified are You, O Allah, and with Your praise, I bear witness that there is no god but You, I seek Your forgiveness and repent to You." Upon departing, one should offer salams to those remaining.