Yes, you are right. I have noticed a tendency for people to "straighten up" when this marking is being done. I'm not sure why. Maybe it's because they are tired of standing and try to keep straight. Or maybe it's instinctual, like when your grandma pinned a hem while your mom was in the dress fidgeting. She would always say, "Stand up straight now." That's exactly what you do not want to do for this situation because it would through off all the hard work you did recreating yourself in every detail, including posture.

I was under the impression that some lines were marked while the form was still on, but then that would be before the 3rd layer of tape.

Yes, you are correct. While you are wrapping the third layer you have to carefully redraw the lines.

Also, with marking of the waist, am I marking my "natural waist" (where I put my hands, as when I'm measuring)?

That depends on what you want marked. I would do the natural waistline, but if you find need to have other markings on your form, you should do the ones that will be helpful to the way you want to use the form.

I don't have a plumb line, so I'm trying to figure out how important this step is and the consequences of not doing so.

You don't need an official plumb line bought at a store. Making one and how to mark is explained in the instructions. The pictures show how to hold it for marking. If you want to skip this step it's totally up to you if you think these markings will not be of use to you.

I like using a plumbline because it lets me make a form that is not only an accurate depiction of the figure but captures the posture of the person as well.