Russian declension

My Russian-English dictionary gives, for “living room”, гостин|ая ой. This genitive singular ending suggests to me that even though the word is a noun, it declines like an adjective….

Neuter noun changes to its genitive form, о —> а, е —> я, but the word сердце its genitive is now сердца , why?

I note from grammatical tables that the feminine genitive, dative, instrumental and prepositional for of the adjective русский is русской, and the equivalent for последний is последней. Suppose I…