Do you check that all the inner cuts are complete before lifting out the design (I use a piece of blue tape) ? As long as you don’t move the work piece or the file in the gui, you can run the cut again and same the piece. I’ve never noticed a problem with the edges after doing so, nor have my clients.
Nope. – search YouTube for “flame polishing acrylic edges” to see numerous examples and tutorials.
My experience is that there’s “flat” then there’s FLAT . A very common gotcha is that even a visually undetectable warping of the material can cause issues. If you tap anywhere on your material and hear a click or an hollow sound, it’s not FLAT .
Your best bet is to cut out a dozen or so Honeycomb Bed Holddown Pins and use them to make absolutely sure your material is firmly secured. I cut out a few from draftboard scraps leftover from various jobs – you cannot have too many of these. 
My cutting success skyrocketed when I adopted these as part of my workflow.
Best of luck!