The environment is a chaotic dynamic system. There are massive non-linearities, phase shifts, etc, and yes, massive damping feedback loops as well. Don't forget the 2nd order, 3rd order, and 4th order effects.
You could build an economic system which did not have periodic crashes, it just would have to be very limited in scope (by keeping it in a highly controlled and isolated environment) and would thus only have one crash, when the containing vehicle breaks apart.
Humans have experimented with very diverse types of economic systems the last tens of thousands of years, and in all cases we have evidence of, there are recurring periods that could reasonably be called crashes.
Some of the fundamentals make that hard to avoid, I suppose: natural events and people's tendency to self-reinforce behaviour within their groups.
I don't think so. The problem is that there's always going to be some amount of speculation in a market. And, it's really speculation that drives prices up beyond what they really "should" be, which eventually leads to the correction. If the speculation goes on too long, and drives prices up too high, then you have a "crash." And, absent regulation to the contrary, there's nothing preventing the market from rising too high, too fast (i.e. the market can remain irrational for arbitrary lengths of time, to paraphrase Keynes). OTOH, there doesn't seem too be a sensible way to determine what constitutes speculation, for purposes of constructing a regulation that prevents it.