Learn Russian: Дельфин плавает вокруг лодки.

Плавать is the multidirectional verb for swimming, while плыть is unidirectional (swimming in one direction toward a specific destination). Because the dolphin is swimming around the boat, its path is circular and constantly changing direction. That makes it a multidirectional action, so we must use плавает.

Why is the word for boat in the genitive case (лодки)?

The preposition вокруг (around) always requires the noun that follows it to be in the genitive case. Since лодка is a feminine noun ending in -а, its genitive form changes the ending to -и.

If the dolphin were just swimming past the boat in a straight line, which verb would we use?

You would use the unidirectional verb плывёт (from плыть) or a prefixed version like проплывает (swims past). Because swimming past something typically happens as part of a single, one-way journey to a destination, it requires the unidirectional verb.

Can I change the word order to Вокруг лодки плавает дельфин?

Yes, Russian word order is very flexible, but it changes the emphasis. The original sentence (Дельфин плавает вокруг лодки) focuses on what the dolphin is doing. If you put дельфин at the end, the sentence answers "What is swimming around the boat?" — treating the dolphin as the most important, new piece of information.