Multiple FF Questions

[Masamune·1600]

Final Fantasy VII

Story-related

-At the end of the game, Sephiroth is destroyed, and so releases Aeris's spirit into the Lifestream, bringing her prayer for Holy to the planet to make it's decision, correct?

Not exactly. Aeris' 'spirit' did not have to reach the Lifestream, so to speak, to unleash Holy. Actually, it seems unlikely that she even had to die for Holy to be cast. Her prayer alone would have been sufficient for the White Materia to glow pale green (which indicates its activation). Indeed, the orb is shown doing so after the Key of the Ancients sequence, which takes place before her spirit reaches the Planet. Recall this segment of dialogue, from the end of Disc 2, which occurs after we see the White Materia has been activated.

Cloud: ......Aeris. She was smiling to the end. We have to do something, or
that smile will just freeze like that. Let's go all together. Memories of
Aeris... ...Although she should've returned to the planet by now, something
stopped her and now she's stuck...... We've got to let go of Aeris' memory.

The implication is, of course, that Aeris had not yet returned to the Planet. Nevertheless, the White Materia was glowing. Holy, then, had been ready long before it was released. However, the actual Magic was being blocked by Sephiroth. Recall this dialogue segment from the Key of the Ancients sequence (as I noted before):

Cloud: Thank you... Aeris. Aeris' voice has already reached the Planet. Just
look at the glow of the White Materia. But...... how about Holy? How come Holy
isn't moving? Why?

Bugenhagen: Something's getting in its way.

Cloud: ......Him...... He's the only one that could do it....Sephiroth. Where
are you?

In essence, Aeris' prayer at the Water Altar was sufficient for the White Materia to be activated. The actual Holy Magic, however, was blocked by Sephiroth (likely due to the influence of the otherworldly JENOVA). Sephiroth's defeat allowed for Holy to be released, to the effects that we saw in the ending FMV sequences.

-Sephiroth never died before the end of the game; Cloud threw him into the Lifestream after he'd been stabbed, correct? But how did Sephiroth become imprisoned in what looked to be giant materia?

The matter of Sephiroth's imprisonment in materia was addressed in my initial post.

After Sephiroth was thrown into the depths of the reactor, his body floated through the Lifestream. Recall that Mako is compressed Spirit Energy and that Spirit Energy is the stuff of the Lifestream; it makes sense, then, that the reactor might tap the Lifestream in order to have a source of Spirit Energy to be converted to Mako. Once in the Lifestream, Sephiroth would have floated to his ultimate location at the Crater. As materia is crystallized Mako/Spirit Energy, and materia can form naturally, Sephiroth merely followed the Lifestream to that point.

When is VII's world referred to as Gaia? That's FFIX!

It's not referred to as "Gaia" in-game, but SE has since clarified that this is in fact the name of the planet. Refer to this site for a brief explanation.