Is it permissible to combine the intention of completing the Quran with the intention of reciting over water in Ramadan? Is it permissible to complete the Quran during prayer? And would this completion be exclusively for prayer, or could it also be the same one intended for recitation outside of prayer?

Slightly spitting (Nafth) into water after reciting the Quran is permissible and lawful. It is permissible to complete the recitation of the entire Quran (khatm) in Ramadan or at other times, along with spitting into water after the recitation. It is also permissible to perform one complete recitation of the Quran for both prayer and recitation. The best form of recitation is that which occurs during prayer.