Learn Russian: Мы живём в квартире семь.

In Russian, when referring to things like apartment numbers, bus routes, or school grades, you often just use the regular counting number (a cardinal number) as a label. So, "apartment seven" is simply translated as квартира семь.

Does the number семь change its ending because it is in a location phrase?

No. Because семь is acting as a label or name for the apartment here, it stays in its basic dictionary form (the nominative case). Only the word for apartment changes to show location.

Why did квартира (apartment) change to квартире in this sentence?

The preposition в (in) requires the Prepositional case when you are talking about a location. For most feminine nouns ending in -а like квартира, you drop the -а and add -е to show where someone is living.

The dictionary form for "to live" is жить. Why does живём have a в in the middle?

The verb жить is slightly irregular. When you conjugate it to match the doer of the action, a в is added to the stem. Then you add the standard "we" ending -ём to get живём (we live).