"Her wine is good."
Translation:Jej wino jest dobre.
No. They are simply copies of the genitive of the respective pronouns, and similar to genitives of nouns, they do not match the possessed noun.
"In linguistics, declension is the inflection of nouns, pronouns, adjectives, and articles to indicate number (at least singular and plural), case (nominative or subjective, genitive or possessive, etc.), and gender. A declension is also a group of nouns that follow a particular pattern of inflection."
'to decline' is just a verb that means inflecting given word for these categories(number, gender, case).
I'm bad with syntax, but "part of the subject" was clearly wrong, and I think that you're right and it's just a part of the predicate.
You can't use the 'to' construction if it's followed by an adjective.
You may think about it kinda like as if "to" was an "=" sign.
"Her wine = a good drink" makes some sense. "Her wine = good" does not.
See here for more details: https://forum.duolingo.com/comment/16373167