I provisioned an AWS EC2 Bitnami for WordPress Multisite AMI which has WP MU DM v0.5.4.3 pre-configured.
I had never heard of this until you posted above.
"Question 1" - primary domain is the URL that DM will redirect the other URLs to. Initially you have at least 2 URLS - the original URL and the domain map. If you want the domain to redirect to the original URL set the original as the primary.
"Question 2 & 3" - if you use the www version then DM will only catch the www version of the domain. If you use the non-www then the www with redirect to the non-www.
"Question 4" - To eliminate unnecessary load on your server for domains where www is the primary domain use a htaccess rewrite rule to redirect the non-www to the www.