Does “a” and “the” for the same noun share the same gendered term?
What I mean is, do all nouns that use “der” also use “ein” and do all nouns that use “eine” also use “die”?
And are there any nouns which, for example use “der” but also “eine”.
Yes, every noun that uses “der” uses “ein”, and every noun that uses “die” uses “eine”. Each noun has an associated gender, which determines which article (der/die/das; ein/eine) is used.
And all plurals are die and so eine except for when it is genitive? I still have a lot to learn.
All plurals are die and thus keine -- regardless of gender.
(There's no positive plural of ein, but the negative kein does have a plural and it inflects like ein otherwise.
You can't use eine for plural if that's what you meant lol. You can see in the word that it was meant for 1 thing (eins), same way you could say for an example 'the cats' but not 'a cats'
Sorry if I misunderstood