I tend to take off the masking with acrylic becasue it’s easier to remove it before than after. I’m pretty good with my settings and can avoid flashback and other marks though so the masking is not really needed. It certainly doesn’t hurt to leave it on though and it gives you a little more wiggle room with your setting. (Some none proofgrade acrylics can come with plastic masking though and you should always remove the plastic stuff. Paper masking can stay.)
Draft setting are just for what it says. If you need to do a quick test for whatever reason, the draft setting are faster to run. Draft-type settings can also work well with other images and graphics too.
I’m not sure what you mean by “smoke”. If there is a white hazing on the edges of the engraving it it has to do with settings and you can get it if the edges get too hot. All acrylic can vary quite a bit in thickness and there’s just no way for PF settings to be perfect for every pice of acrylic. Leaving the masking on can help with it or you can play with the setting to dial them in better to avoid it. (And once the hazing is there, you really can’t gt rid of it.) If by “smoke” you mean those little dots on the draft ones, that’s the GUI processing the background and converting it to dots. If you change it to “vary” setting like in your first engraving, the white background would be totally ignored and not processed.
Remember that the quality of your scanning can make a big difference. (Basically it’s garbage in, garbage out.) If it were me, I’d save the scan as a PNG with a transparent background with a high resolution. (Other types can work well too, PNG would just be just my preference for your project.) You might also want to do a forum search for “defocusing” acrylic and give it a try. It really helps with soothing out acrylic engravings.