Hello. Here are your answers:
1. With Community Builder integration, you can have the standard fields like name, address, city, state, zip, phone and email auto-populate into registration forms. This would not apply to custom fields like birthdates and such. Also it would not apply to members of a group registration, but only to the final billing page of the group registration. In our new 2.6 release (coming in a few days), you'll have the same type of feature with JomSocial.
2. DT Register is used by thousands of Joomla sites and there have definitely been some sporting sites. A couple possible related examples might be:
http://www.pilates4fitness.com/mat/online-registration
http://www.allmetrosports.com/index.php?option=com_dtregister
3. You can create a custom field checkbox something like "Is the registrant between 3-6 years old?" If they mark it, then they can proceed. If the field is marked as required, they won't be able to proceed without selecting that option.
Hope that answers your questions. Thanks.