I don't follow why you would end up with children within
children.
You could use the structure I propose but without the
redirect. Just make sure that project has no links to or from any
child project. Your existing parent then becomes a child like all
the others. I believe that would work for CHM output as well.
However, you say you have few parent / child links so you can
live with what you have.
That sort of brings us back to your original questions. Your
different structure will not affect those points so you should be
able to glean those answers from the topic.
See my previous answer re the project name. The child opening
in a new window sounds like you are pointing to its start page,
rather than the topic your want displayed. Come back and clarify
those issues if not resolved.
Help others by clicking Correct Answer if the question is answered. Found the answer elsewhere? Share it here. "Upvote" is for useful posts.