Learn Russian: Огромная толпа стояла вдоль дороги.

The preposition вдоль (along) always requires the Genitive case. Since дорога (road) is a feminine noun ending in -а, its Genitive form changes to -и.

Since толпа (crowd) refers to many people, why is the verb стояла in the singular?

In Russian, verb agreement is strictly based on the grammatical form of the noun, not its meaning. Толпа is a grammatically feminine singular noun, so it takes the feminine singular past-tense verb стояла.

Can вдоль only be used for stationary positions like standing (стояла)?

No, вдоль works for both static position and movement. Here it describes a stationary line of people, but you could also say шла вдоль дороги (walked along the road) to describe movement parallel to the road.

Why does the Genitive form of дорога end in -и instead of the standard feminine Genitive ending -ы?

This happens because of a fundamental Russian spelling rule. After the consonant г (as well as к, х, ж, ч, ш, and щ), you must always write и, never ы.