Learn Russian: Маяк стоит на скалистом острове.

In Russian, vertical objects like buildings, monuments, and lighthouses are often described as standing (стоять) rather than just being located (находиться). It gives a more vivid, natural picture of the lighthouse rising up from the island.

How do we know if стоит means stands or costs in this sentence?

Context makes it obvious, but they also sound different because of word stress! Stands is стои́т (stress on the ending), while costs is сто́ит (stress on the root).

Why is it на скалистом острове (Prepositional case) instead of the Accusative case?

The preposition на takes the Prepositional case when describing a static location answering the question 'where?' (like the lighthouse already being on the island). If the sentence described motion toward the island (answering 'to where?'), we would use the Accusative case: на скалистый остров.

Since this lesson is about defective verbs, does стоять lack a 1st-person singular form?

No, стоять is a fully regular verb in that regard. It has the 1st-person singular form я стою (I stand). The defective verbs you are learning about (like победить or убедить) lack the я form due to awkward historical phonetic combinations, which isn't an issue for стоять.