I'd stay away from any of the built in controls (i.e. DetailsView, FormView) for anything other than simple CRUD forms, as it's not much more effort to manually create your own data-entry forms.
Dynamically adding controls to an ASP.NET Webform (and have them work across postbacks) is quite a tricky one to get right, but in short you'll need to do something like:
- Add a table server control which will store your dynamic rows.
- Create a property (stored in ViewState or ControlState) to store a count of rows available.
- Handle the appropriate 'add' button click event, to increment the count property and add a new table row, and child controls.
- Inside an OnInit event, create the number of table rows stored in the count property.
Dynamically created controls aren't persisted across postbacks, so you'll need to create them on every postback during the pages OnInit method. As long as the controls are recreated in the right order and with the same ID's, then they will be repopulated successfully on postback.
Because you're dynamically adding controls, you may need to set the pages EnableEventValidation property to false.