🚀 go-pugleaf

      and as a general question for learning, how can I learn all about how
      to put lines in the design space for purposes of joining these lines,
      curving any part of one or more lines and then filling or outlining the
      finished shape made from joined lines?




Well, you can read the documentation. That will be much more thorough and methodical than asking a random series of "how do I..." questions in a user forum. And it will take you a lot less time.

      Using my Windows program (not an Adobe product)




You can say the name. If there's actually anyone here who doesn't know other drawing programs exist, well, they need to. Your description sounds like Xara Xtreme.

      I want to end up with a shape that is similar to one-quarter of a full
      moon..create a line...convert that line to a curve...drag from the midpoint
      of the line and have it become an arc...select one of the endpoint nodes...
      "auto-close"...double-click near the midpoint of the straight edge to
      add a new node..."convert to curve"...drag...




A similar procedure could be used in just about any vector drawing program that draws cubic Bezier curves. A much quicker procedure could also be used in just about any program, by leveraging the geometric shape tools and path combination commands that are just as ubiquitous:

1. Draw a circle.

2. Duplicate the circle.

3. Overlap the circles partially.

4. Use one circle to "punch" the other, leaving the difference (the crescent shape).

Here are two AI-specific differences I note in your description:

Illustrator can't bend a straght segment by dragging its middle if the straight segment has both its associated curve handles retracted. Dragging such a segment in AI just moves the segment (and its associated anchorPoints).

Illustrator displays fills on open paths. There is no option to turn off that often unwanted behavior.

Again, read the manual (the online Help files). It will take you decades to learn the program by asking random questions on the basic use of the tools, location of commands, organization (well, disorganization) scheme of the program, etc., etc.

JET