Hi Frances and thanks for helping Sid out... Just a few comments on your points.
1.- In Moodle, a Lesson is a self-contained activity, which contains quiz-type questions of its own. There is nothing "illogical" in its behavior. I would certainly advise against having inside a lesson a link to a quiz, as this may lead to unpredictable behavior of the lesson itself...
3.- It is not required for one Lesson to be dependent upon the completion of another that both lessons reside in the same Course Topic.
4.- There is no "progress bar" that would show a Moodle Course "progress". However, in Moodle 2.0 (the latest version available) it is possible to mark activities as "completed". See the documentation page at Course completion tracking settings.
5.- "I think you can be alerted when students complete a quiz,..." Yes, this is part of a Quiz" Permissions" settings : it's called "Get email notification of submissions" and can be switched ON or OFF by a teacher.
If I may share my experience of teaching with computers for 25 years, including teaching with Moodle for the past 6 years or so, I would advise Sid, the OP, to start with finding out what is possible to do with Moodle, rather than to start with an a priori course design and find out that Moodle cannot do what that design wants to do. Most of Sid's needs can be met by using Moodle (especially version 2.0), but Moodle is not really suitable to build "rigid" programed instruction which forces students along a pre-determined path, as you will find out...
All the best,
Joseph