Yes, I think so: What you are looking for is either a Parent - Response hierarchy, or something very similar. If that is what you have in mind, Parent-Response is done automatically using a $REF field (You should normally not declare this field, it's all built-in as default...)
I often use this structure COMBINED with a separate UNIQUE field (Computed when composed) to make the add'l keys for search. Notes have very good built-in methods for keeping track of response documents, but I also prefer to use keys that is slightly more readable than a 32 character key; So I use the @UNIQUE function to create those keys. I also set this field to be inherited into the response + I give the response a separate unique value (1 common main key for the structure + unique key pr response)
To copy all fields from one to another, depends on the settings for the response document. On the second tab (form properties, the one looking like a hat with a 'propella' on top) the first tick box 'Formula inherit values from selected document' will bring in the values of the fields with the same names. Make sure to declare the fields you want brought over inside the response document. If you want a link back to the parent document, create a rich text placeholder for this...
I suggest you read a bit about Parent-Response hierarchy in the Notes designer help. It is well documented but a bit 'large' so there will be some help documents to look into, but it could give you definetively better answers than what I can squeeze in here...
Brgds,
TrooDOS