Вчера мы увидели в воде медузу, а чуть дальше — дельфина.

Because увидели is from the perfective verb увидеть, which is used for a completed event: we caught sight of / we saw.

In this sentence, the idea is that yesterday there was a specific moment when we saw a jellyfish, and then farther away, a dolphin. Russian often uses the perfective here because the action is viewed as a whole, completed event.

By contrast, видели would come from видеть (imperfective) and would more naturally suggest something like:

• we were seeing
• we used to see
• we saw in a more general or less event-focused way

So увидели is the most natural choice for a one-time sighting.

Увидели is:

• past tense
• plural
• from the infinitive увидеть

It agrees with мы (we), so it has the plural past ending -и.

Compare:

• я увидел / увидела = I saw
• ты увидел / увидела = you saw
• мы увидели = we saw
• они увидели = they saw

Russian past tense agrees in number, and in the singular also in gender.

Because медузу is the accusative singular form, and it is the direct object of увидели.

The dictionary form is:

• медуза = jellyfish

But feminine nouns ending in -а usually change to -у in the accusative singular:

• медуза → медузу
• мама → маму
• девушка → девушку

Since the sentence says we saw a jellyfish, Russian uses the accusative.

Because дельфина is also accusative singular, but masculine animate nouns behave differently from feminine nouns.

For masculine nouns:

• if the noun is inanimate, accusative usually looks like nominative
• if the noun is animate, accusative usually looks like genitive

So:

• дельфин = nominative singular
• дельфина = genitive singular
• and also accusative singular because дельфин is animate

That is why:

• Я вижу стол = I see a table
• Я вижу дельфина = I see a dolphin

This animate/inanimate distinction is very important in Russian.

Because в with a location meaning takes the prepositional case.

Here, в воде means in the water, so it answers where?

The noun is:

• вода = water

Its prepositional singular form is:

• в воде

Compare:

• в воде = in the water, in the water area
• в воду = into the water

So:

• увидели в воде медузу = saw a jellyfish in the water
• if there were movement into the water, Russian would use a different case

Чуть дальше means a little farther, a bit farther away, or slightly farther on.

• чуть = a little, slightly
• дальше = farther/further

Together, they form a very common expression.

Examples:

• чуть лучше = a little better
• чуть позже = a little later
• чуть дальше = a little farther

So in this sentence, it means that the dolphin was seen a bit farther away than the jellyfish.

Here а is a connector showing a mild contrast or shift of attention. Depending on context, it can sound like:

• and
• while
• but
• and then

In this sentence, а does not express a strong contradiction. It is more like:

• we saw a jellyfish in the water, and a little farther away, a dolphin
• or ... while a little farther away, there was a dolphin

So а helps move from one sighting to another with a slight contrast in location.

The dash shows that something has been left out because it is understood from context.

The full idea is something like:

• Вчера мы увидели в воде медузу, а чуть дальше увидели дельфина.

Russian often omits repeated words when they are obvious. The dash marks that omission.

So the second part really means:

• and a little farther away, [we saw] a dolphin

This is very natural in Russian and often sounds smoother than repeating the whole verb phrase.

Yes. A fully expanded version would be:

• Вчера мы увидели в воде медузу, а чуть дальше увидели дельфина.

That is grammatically correct. But the version with the dash is often more elegant and natural because it avoids unnecessary repetition.

Russian frequently uses this kind of ellipsis, especially in writing.

Russian word order is flexible, and this order sounds natural because it presents the information in a clear sequence:

• Вчера = sets the time first
• мы увидели = gives the action
• в воде = gives the location
• медузу = gives the thing seen
• а чуть дальше — дельфина = adds a second sighting

A different word order is possible, for example:

• Мы вчера увидели в воде медузу...
• Медузу мы увидели вчера в воде...

But the original sentence is a very normal storytelling order.

No. Вчера is an adverb, not a noun, so it does not change for case.

It simply means yesterday and stays the same:

• Вчера мы были дома.
• Я видел его вчера.

So even though Russian nouns change a lot, words like вчера do not.

Because в воде means in the water, which fits animals like a jellyfish and a dolphin.

• в воде = in the water
• на воде = on the water, on the surface of the water, or sometimes related to water transport/sports

So:

• медуза в воде = a jellyfish in the water
• лодка на воде = a boat on the water

In this sentence, в воде is the natural choice.