Learn Dutch: Het meisje loopt naar de supermarkt. - The girl walks to the supermarket.

In Dutch, naar is the standard preposition for movement or travel toward a destination. Whenever you are going to a building, a city, a country, or a person, you will almost always use naar.

Could we use in instead of naar if she is going inside?

If you want to say she walks into the building, you would use in, but it actually moves to the very end of the sentence (loopt de supermarkt in). For now, just remember that naar is the best word when you are simply heading towards a destination.

A girl is female, so why does the sentence use het meisje instead of de meisje?

All Dutch words ending in -je are diminutives (words for small things). Every single diminutive in Dutch is a het word. Because of this strict grammar rule, meisje takes het, even though it refers to a female person.

Does loopt only mean "walks"?

Usually, yes! However, in the Netherlands, lopen can sometimes also be used to mean "to run" depending on the situation. If you need to be completely clear that someone is running, you can use the specific verb rennen.