Do we live in a postmodern period that is fundamentally different from a modern one?

To be absolute--yes, because 'modernists' did not shun the idea of 'knowing that one knows', as post modernists do:

"Postmodernism is difficult to define, because to define it would violate the postmodernist's premise that no definite terms, boundaries, or absolute truths exist."

http://www.allaboutphilosophy.org/postmodernism.ht...

So the answer to your question is a 'modern' one. A post modernist answer would be such as, "Maybe, maybe not; who can say?"

If the American colonists, or Abraham Lincoln, were post modernists, there would not have been the US because that Congress agreed on absolute truths: "We hold these truths to be self-evident...", and Lincoln would have been wishy washy, believing the south might be right about slavery.

Yes. the postmodern period is after World War 2. It is different from the modern period in that it fosters a skeptical view of the arts, a depressive view, due at least in part to the overwhelming loss of life in the World Wars..

The answer is live in the now and **** the what ifs.