Learn Swedish: Kartan som hon tittar på visar västra Nordamerika. - The map that she looks at shows western North America.

Normally, when you put an adjective before a definite noun, you need the free definite article (den, det, or de). However, geographical proper nouns like Nordamerika are a special exception. We skip the free article, so we just use the adjective directly before the name.

If we skip the free article, why does the adjective västra still end in an -a?

Proper nouns are treated as inherently definite in Swedish. Because of this built-in definiteness, any adjective that describes them must still take the definite -a ending, which gives us västra instead of the base form väst.

Does the verb visar break the V2 (verb-second) rule since it is the sixth word in the sentence?

It actually follows the rule perfectly! The entire chunk Kartan som hon tittar på acts as one big subject block. Because that whole block takes up the first position in the main sentence, the verb visar correctly sits in the second position.

Can I put the preposition på before som instead of leaving it at the end of the clause?

No, you must leave it at the end. The word som is extremely common but has a strict rule: it can never have a preposition directly in front of it. Placing the preposition at the end of the clause works just like saying "that she looks at" in everyday English.