I am not too familiar into postmodern philosophy, however, I read some summaries and reviews that state that many postmodern thinkers reject and disparage the modern ideas springed from Enlightenment, such as the Lockean natural rights and Mill's harm principle, and even Kant's general outlook of universality. What kind of political regime would postmodern philosophers propose? What is the pursuit of philosophy according to them?

Postmodern philosophy claims to be especially skeptical about simple binary oppositions that allegedly dominate Western metaphysics and humanism, such as the expectation that the philosopher may cleanly isolate knowledge from ignorance, social progress from reversion, dominance from submission, or presence from absence. This is sometimes called anti-foundationalism. To some critics, this skepticism appears similar to relativism or even nihilism. Defenders of post-modernism would argue that there is a distinct difference, however: while relativism and nihilism are generally viewed as an abandonment of meaning and authority, postmodern philosophy is generally viewed as an openness to meaning and authority from unexpected places, and that the ultimate source of authority is the "play" of the discourse itself (rather like Adam Smith's invisible hand of the market).

Whether postmodern ideas developed independently or were influenced by the uncertainty associated with quantum physics, I do not know.

It tries to show that the sources of Knowledge that we take as being secure as much more tentaive than we first assumed. Particular attention is paid to language in the postmodern movement with postmodernism having strong links with deconstruction & poststructralism.

They both developed in the same era, but my reading of modern and postmodern philosophers (Levi-Strauss, Lyotard, Derrida, a couple others) seems to definitely want to distance itself from any assertions of understanding (as might come out of a natural science).

I think Bertrand Russell, who was more "modernist" than "postmodernist", comes the closest to the quantum physics mentality by literally trying to break down mathematical and linguistic logic to its essential (atomic, as he called it) constituents.

In this, I needn't remind you, that Heisenberg uncertainty is a cardinal but very small part of quantum physics. .

The uncertainty principle doesn't tell us anything at all about quantum behavior or quantum particles,

it only tells us what we can know and what we cannot.

The nature of elementary particles is quite easy for physicists to measure --

they just cannot measure a single individual one.

Imagine that we can't study a single baseball, but we can fire them through a pitching machine and based on their average impact learn their mass and based on their point of impact learn their spin. Furthermore, Heisenberg's uncertainty has never been universally accepted with some famous examples.

I think that basic scientific advancements were simultaneous but largely coincidental branches from this same trunk.

A single read of what is happening in any of these worlds, by an astute observer, can immediately begin a chain reaction of thoughts that begin to germinate into a whole new line of thinking. Happens to me all of the time.

Only Russell, did have a Heisenberg there to articulate the Uncertainty Principle, which might have saved Russell lots of time in his endeavor to create certainty in linguistics.

Yes, that can happen, but that's different than did it happen.