I have had to cut your original question down to focus on one point only according to enotes regulations. This is a great question however because by focussing on paradoxes in the text you are raising a far bigger and more important issue which is how signs and actions are interpreted. One massive example in the text is how the "A" that Hester is forced to wear as a mark of shame is actually changed or transformed into a badge of pride - Hester shows that she is able to not let meanings that others give to symbols determine with authority the definitive meaning and that she is free to determine the own meaning that she gives to symbols.
This issue of paradoxes and how they are treated in the novel thus relates to the importance of point of view. No facts in this novel are given definitive interpretation. Even the death of Dimmesdale, following the revelation of his guilt at the end of the novel, is read by eye-witnesses in a number of different ways according to their own particular bias. Signs might be described with great precision, but the way in which they are read depends upon a larger context, according to the knowledge and experience of the reader. The relativity of understanding makes tolerance and compassion moral imperatives for Hawthorne.
So this perhaps is the ultimate paradox - Hawthorne in this text gives us a number of key symbols that almost demand to be interpreted, yet at the same time through the text he shows us how dangerous it is to assume any one definitive interpretation of a text. We are left convicted of our desire to make meaning out of symbols, but also the dangers implicit in such an act.