Am trying to save questions to case properties in a registration form. Am able to do this for all questions except those that involve lookup forms or those with hidden values linked to lookup forms. These questions don't appear on the list of questions so I can't select them.
That sounds odd, you should be able to save those properties.
Are those questions inside of a Repeat question group, by any chance? Those questions can't be stored into a Case without first transforming them into a single value (or being stored into child cases).
Is it possible to remove the 'name' property? Whatever I'd like to set to the 'name' property is already under the child case so I don't need it for the first bit.
Some value is required for the name property so that the system has a value to display in reports, exports, and other areas that need a summative name to display for the case.