[the phantom]

it is understandable that Sauron would not fear the destruction of his Ring. He thought it had already been done.

Do you really think it's possible that Sauron didn't understand the way his own Ring worked?

but that does not mean that he would not have gained a greater understanding of how things worked

I just find it hard to believe that Sauron could gain understanding about something he should've already known everything about (or almost everything, certainly more than anyone else).

But I'm willing to play with what I think is sort of silly. So, let's assume that Sauron didn't have a clue about the most basic aspect of his Ring (whether or not it would kill him if it was destroyed). In that case, perhaps Sauron wasn't really afraid when he sensed Frodo in Mt Doom. Perhaps the historians of Middle Earth interpreted the tremor that ran through his empire as fear, but in fact he was overjoyed and excited to finally find his Ring (and so close to home), and was so anxious to get his precious that he stopped focusing on everything else in his empire. After all, so what if his servants were afraid without his will behind them, for within minutes he'd have his Ring on and he'd be victorious.

So there's another way to piece together the quotes I gave (and once again, it would make Gandalf very wrong about Sauron).

He fled after his defeat and assumed that the Alliance had destroyed the Ring

But, no worries, who in their right mind would wish to destroy the Ring?

Those statements don't work as I said in my first post. It's impossible that Sauron would think someone destroyed his Ring and yet never think of the possibility that someone would destroy his Ring. That contradiction is too extreme to explain away. One of the statements that Gandalf made was not true. I would guess the first quote I gave in my first post would be the inaccurate one.