What is the ruling on the succession of vows involving prayer and adjusting them by increasing the number of rak'ahs based on the importance of the need, taking into consideration praying some of these rak'ahs quickly and counting the regular sunnah prayers among them?

There is no harm in praying the vowed Rak'ahs during the Duha (forenoon) time, or before and after Dhuhr (noon), or between Maghrib and Isha (dusk and night) prayers, if they are performed with the intention of fulfilling the vow. There is no harm in performing them quickly as long as tranquility (طمأنينة) is achieved. However, performing them at a speed that does not allow for tranquility is not permissible. There is no objection to delaying some parts of the vow if one is unable to complete it, and it is obligatory to fulfill it, even if in separate parts, unless one intended for it to be continuous.