I shall try to answer this question, but it is so badly posed as to be nearly unintelligible.
What do you want to say? (Remember that "component") may be used as a noun or an adjective. So the short answer is
If "component" is being used as an adjective, adjectives have neither possessives nor plurals.
If "component" is being used as a noun, both possessives and plurals of all but a handful of nouns end in an s sound, but in writing we distinguish between regular plurals (no apostrophe), singular possessives (apostrophe before the s), and plural possessives (apostrophe after the s).
What the proper form is depends on the intended meaning. I have no idea which of the following you intend
the fields of the component form
the fields of the component forms
the fields of the form of the component
the fields of the form of the components
the fields of the forms of the component
the field of the forms of the components
None of those makes much sense without a context, which is completely absent. Assuming that each does make sense in some context, they are expressed using the possessive as
the component form's fields
the component forms' fields
the component's form's fields
the components' form's fields
the component's forms' fields
the components' forms' fields
As I say, none of those makes much sense without context, but the grammatically correct way to write it depends on what meaning is to be conveyed.
The discussion about "generic nouns" is obscure. Except for proper names, every noun is generic in that it describes a class of things or concepts. Perhaps you are thinking about the difference between count nouns and mass nouns. If so, that difference is not germane because "field," "form," and "component" (when used as a noun) are all count nouns.
Your example about "department" may indicate that you are thinking about collective nouns. But your example has nothing to do with possessives and simply reflects the difference between singular (one HR department) and plural (more than one HR department).