Does pausing at every word of Al-Fatiha invalidate the prayer, or does uttering (اهدنا الصراط المستقيم - Guide us to the straight path) without the "alif" when reciting it continuously [with what precedes or follows it] invalidate it?

When connecting recitation, the Hamzat al-Wasl (connecting hamza) is not pronounced. "Ihdina" (guide us) begins with a Hamzat al-Wasl, so your action of not pronouncing the alif when connecting is correct. Even if you were to start with "Ihdina al-sirat" (Guide us to the path) and did not pronounce the Hamzat al-Wasl, your prayer would not be invalidated. However, the correct way is to pronounce it when starting. Stopping after every word in Al-Fatihah does not invalidate the prayer, unless it leads to a grievous linguistic error that distorts the meaning. Nevertheless, this method is not considered proper recitation because it results in an impermissible and ugly stop (Waqf Qabih).