Firstly, In order to use the FamilyManager class you must querying a family document.
The API docs description of what the FamilyManager class is:
“The family manager object to manage the family types and parameters in family document”.
Secondly, all family types within a family document have access to the same parameters. Therefore the .parameters property will return all of the parameters in a family document. Within which, each family type can have different values against the same parameter. Rather than tying to get the individual parameters from each family type as you are.
For example (ignore python node header name, ripped code from another project):
To start wading into the weird ether world which is API family document parameter values and types etc it is definitely worth looking at the forward iterator method (warning, its a touch confusing!).