1) What special qualities of these new lamps make them able to
withstand the destruction that came to the others? Can they be
considered "better" in a way?

Ummm, not made of ice, presumably. Maybe the lamps themselves are not better, but they are protected by powerful entities rather than just sitting there by themselves. They are also physically removed from the surface of the Earth, and provide a moving target. So not better, but adapted to an environment that the Valar now understand better.

2) It seems that each creation of a light source is somewhat inferior
than its predecessors. Is this merely an expression of nostalgia and
regret of later generations looking back to a perceived "golden era"?
Or does it represent a true downward trend in creation -- moving from
more perfect to a flawed form?  Is this how elves see history? Is this
how Tolkien sees history?

Notions of entropy and progress are both encompassed, I suppose. As discussed lower, Melkor could embody entropy and Eru energy, so the conflict between the two is what actually exists in Middle-earth. Thus some things get better (eg some Men) and some things fade, without actually losing identity or beauty (Elves). The light issue seems to peak with the trees, but they had their flaws, too, given that they only really lit Aman. So there's a bit of up, a bit of down, some compromise, some improvement. It's part of what makes Tolkien's work more interesting than so many incredibly linear or two dimensional fantasy imitators.

3) What of the notion of progress and improvement from one generation
to the next?  If the view of a slow downward spiral is accurate, what
can be expected for the future? What of hope?

The hope of keeping what is good, and improving what is not. This hope is never seen as futile in any of Tolkien's works, I think. It might not be forever, but it is up to us to do what we can (as Gandalf says in LOTR) with the time we are given. Same as Galadriel and Elrond and Cirdan try to do.

"Like Bentham's Panopticon, Sauron's power and authority is placed in the discipline of surveillance a la Foucault."