Modernism, besides being a reaction to past literary movements, is also something that developed from the discoveries in the fields of science and psychology. The theories of Darwin about the evolution of humans made humans question the 'ultimate truth' known to them- GOD. The Victorian morals were questioned. The literature of the late Victorian era and the Early Modernism depict that.

With the occurance of the world wars, people lost their trust in truth and faced 'existential angst'. Nietzsche's words "God is dead" seemed to be the only 'truth'. My point here is that Modernism is more of a reaction to things happening in the modern society and an expression of what the modern man was going through. Writings of Joyce, Woolf, Kafka, Camus represent that perfectly.

Truth in the post modern era became individualistic. It was no longer indisputable. Fundamental truths were replaced by a kind of relativity of truth, depending on where you stand and what you are looking at.

Most Modern fiction leaves the ultimate meaning of the work more open to the reader's interpretation rather than ending with what I would call a perfect package with a perfect "bow-tied" ending. There is a sense of ambiguity in Modernism that lets the reader determine the "truth" of the work for him or herself.

First, I don't think we can find any literature that is not responsive or reactive to the past, literary history, artistic precursors, etc. Even the science fiction of the 20th century was reacting to the adventure stories that came before it (Westerns, Pirate stories, Military epics, etc). So, yes, modernism was a response to earlier literary movements. (...maybe you have something more specific in mind with your question regarding "a reaction to traditional literature" that I am not seeing right away...)

Secondly, modernism, as I understand it, was the first literary/arts movement to present the notion of subjective truth as a replacement for absolute "real" truth. Truth became defined by personal experience in modernism, which also emphasized a personal relationship to history. 

Postmodernism and modernism are not completely different in their regard for and presentations of truth. 

Look at the modernist works like Faulkner's As I Lay Dying and you see a work with many perspectives on truth and reality. Look at Hemingway's Sun Also Rises and you see a very personalized understanding of moral truth, social truth and hopeful truth. 

My answer to both of these questions would be "yes." From what I understand, modernism came about in part due to a rejection of traditional thinking and to make what was old and outdated new, contemporary, and relevant. I do think that modernist thinking only accepted certain truths. If something did not fit into the accepted truth, then it was rejected. Postmodernism, as I understand it, seems to be an "anything goes" type of philosophy as long as you can defend it.