A. Yes, you can do this. There are two options:
1) Have them purchase the domain from your site or have them import the domain. This can be done from /admin/domains.php. If done this way then the member can setup directories and assign pages from /admin/pages.php to the directories and for the home page.
2) Have them setup their domain name to forward to the capture page.
A. A piggyback domain can be added to the system, and then it can replicate for the member. However, the piggyback has to be hosted on our server (not on the member's own hosting account). Also, members can use forwarding with masking (or frames) to do a similar affect (this can be done through the company they purchased their domain name from).
A. Yes, it will still pick up the variables within your software.
The piggy back domain is an additional domain added to your current software and will utilize features and aspects of your current software.
A. No, typically when changing a domain name you do not need to modify any of your content. The only time you need to is if you have any URLs using the full path of the old domain, then the URL (exa: links) would need to be fixed.