Learn Hardcore Russian: Мой дом находится именно здесь.

In Russian, the present-tense copula есть is usually omitted, and to express location you typically use verbs like находиться, лежать, стоять.

находиться (to be located) is the most neutral way to say “is located.”
есть appears mainly to mean “there is/are” in existential sentences, not for precise locations.
Omitting the verb entirely (“Мой дом здесь.”) is understandable in casual speech but sounds informal and relies heavily on intonation.

What case is дом in, and why?

Дом is in the nominative case because it is the grammatical subject of the sentence (“my house”). Location adverbs like здесь don’t govern a case on the subject; they simply modify the verb.

Why is the possessive pronoun мой used and not моего?

Мой is the nominative masculine singular form of “my,” matching дом (a masculine noun in the nominative). моего would be the genitive case, which would be used in contexts like “end of my house” (у моего дома), not here.

What role does именно play in the sentence? Can I leave it out?

Именно is an emphasis particle meaning “exactly” or “precisely.” It highlights that the location is spot-on: