1. I agree with Stuart that the last couple of decades have been a period of immense expansion of capitalism. With hindsight, I think the long upswing started before the collapse of the Stalinist states.
2. I'm very dubious about the "long waves" theory. I just don't know about the current downturn. There are some reasons for supposing that the downturn in trade and production will be less spectacular than the financial collapses, but I don't think you can deduce that just from the "nature" of the (long) period.
3. Yes, in the Grundrisse Marx wrote that the tendency of the rate of profit to fall was "in every respect the most important law of modern political economy..."
I think he was wrong about that; I think the more elaborated (though still unfinished) exposition in Part III of volume 3 of Capital is flawed. But even if I am wrong about that, the facts remain:
a) Whatever about Marx scribbling into his private rough notes (maybe in the small hours of some morning) that the tendency of the rate of profit to fall was "the most important law of modern political economy", he never mentioned it in anything he completed for publication. If it was really his settled opinion - not just a scribbled flourish - that this tendency was so important, why did he not mention it somewhere for publication? Visibly he put a lot of stuff into Capital volume 1, and into Wages, Price, and Profit, that would belong later in a complete exposition, and made a point of at least alluding to other stuff he considered important (e.g. formation of prices of production). Or he could have written an insert on it for Anti-Duhring. He didn't.
b) Part of the answer is that for Marx, Capital was not a work of "political economy", but of "critique of political economy". His scribbled flourish dubbed the TRPF the most important law of "political economy", i.e. of orthodox, mainstream, bourgeois economics. It was not at all the most important of Marx's own "economics".
c) No wonder that Marx, finding so many orthodox economists subscribing to a proposition that capital would eventually run out of momentum, was elated by it, and inclined to seize upon it. But that does not give great theoretical weight to it.
d) In any case, Marx does not mention the TRPF in his most substantial and connected writings on capitalist crises (TSV II and Capital II, as I mentioned above). In the Grundrisse itself, the reference to the TRPF is separated from the discussion on crises (pp.401-447). If Marx thought the TRPF was important, it was not for crisis theory that it was specially important.
In the bit on the TRPF in Capital III there is a short passage suggesting that the TRPF may trigger crises through its specific effects on smaller capitals. But the suggestion is visibly half-hearted; unconnected with Marx's main writings on crises; and, anyway, I submit, not true to the facts of crises.