Hello. DT Register offers a much more extensive package than the other extensions you have mentioned. EB just steals from DT Register... and ERP has just fallen way behind in overall functionality.
You would use our "Detailed Group Registration", meaning you'd enter data for member 1, member 2, etc... then finish with the billing/contact info for the group. You could have the child names and other details for each member, then put the parent name, address, etc for the group contact.
When you integrate with Community Builder or JomSocial, you can sync any profile field with any DT Register field so data is auto-populated when the user is logged in. So either have the user login prior to registering for the event... or use our auto-user creation feature, which allows them to create the login DURING the event registration. They would also setup their CB or JS profile so their data is there for auto-populating next time they return.
You can create conditional fields so field X only displays if the user chose the appropriate option in Field Y. Auto-populating based on a selected or input DATE isn't currently supported though. Field selections can have limits on how many times they are allowed to be selected and can also modify the overall price of the registration with fees and discounts (either $ or %).
For a digital "signature", what most people do is have a required checkbox that you check saying you agree with some set of provided verbage. You can also have a required input box saying something like "By entering your initials in this box, you agree that... blah, blah..."
There IS a backend demo (although messy usually as people do all kinds of testing there) at:
http://www.dthdevelopment.com/demo/administrator
user: demo1
pass: demo123
Our field structure is more flexible than any other Joomla event system. You can make as many fields as you need to and I've already stated some of the cool elements that you can do with them. You then select which fields are used for each event, which are required, etc.
The form itself doesn't have a print function, but you customize the email that the user receives after registering, which will dynamically include data from the registration using the wide array of email tags available.
DT Register works the same with CB or JS... not one is better than the other on this end. You'll just need to research them and see what other features matter more to you on the user profile and social aspects for your site. Thanks!