Learn Russian: Наш дом далеко.

In Russian, the present tense of the verb "to be" is almost always skipped. So, instead of saying "Our house is far", you literally say "Our house far" (Наш дом далеко).

Why do we use наш instead of наша or наше?

Наш means "our", and it must match the gender of the noun it describes. Because дом (house) is a masculine word, we use the masculine form наш. If we were talking about a feminine word like машина (car), we would use наша.

Does the word далеко change its ending because дом is masculine?

No. Далеко (far away) is an adverb, meaning it tells us where something is. Unlike adjectives, which change their endings to match masculine or feminine nouns, adverbs in Russian never change their form.

Why don't the first two "o" letters in далеко sound like a standard "o"?

In Russian, the letter "o" only makes a true "o" sound when it is stressed. In далеко, the emphasis is on the very last letter. Because the first two "o" letters are unstressed, they are pronounced more like a short "a" or "uh" sound.