Does the prayer become invalid if the recitation ends with the beginning of bowing, or if the beginning of rising from bowing/prostration coincides with the end of the glorification, on the claim of combining one pillar with another?

The Fatihah must be recited in its entirety during the standing position (qiyam); reciting only part of it during bowing (ruku') is not sufficient. As for surahs other than the Fatihah, their recitation is sunnah (recommended). The obligatory amount of standing is that which allows for the recitation of the Fatihah; anything more is not obligatory. According to the Hanbalis, it is obligatory to pronounce the takbir of transition (takbirat al-intiqal) while moving between postures, and to say "Sami' Allahu liman hamidah" (Allah hears those who praise Him) during rising. If one bows while still reciting, or rises while still glorifying Allah, until they have fully reached the next posture, and intentionally fails to pronounce the takbir of transition, their prayer is invalid according to them.