У моря мы увидели чайку.

Because the preposition у requires the genitive case.

The dictionary form is море (sea), but after у it becomes моря:

• море — nominative singular
• моря — genitive singular

So у моря means by the sea / near the sea.

Here у means by, near, or next to.

It does not mean possession here, even though у is also very common in sentences like:

• У меня есть книга — I have a book (literally, At me there is a book)

In у моря, it is purely a location phrase: by the sea.

Yes, but the meaning changes a bit.

• у моря = by the sea, right near the sea/coast
• на море = at the sea / seaside, often used more generally, including the idea of being at the coast or on a seaside trip

So in this sentence, у моря gives a more exact sense of location: the action happened by the sea.

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

The basic form is:

• чайка — nominative singular

But after a verb like увидели (saw), the thing seen goes into the accusative:

• увидели чайку — saw a seagull / gull

For most feminine nouns ending in -а, the accusative singular changes -а to -у:

• чайка → чайку
• девушка → девушку
• книга → книгу

Because увидели is perfective, and it fits a completed event: we saw / caught sight of a seagull.

• увидели = saw, caught sight of, a completed action
• видели = saw / were seeing / used to see, more process-like or general

In this sentence, the idea is that at a certain moment, we spotted a seagull, so увидели is the natural choice.

Увидели is the past tense plural form of увидеть.

Russian past tense agrees with the subject in number and, in the singular, also gender:

• я увидел / увидела
• ты увидел / увидела
• он увидел
• она увидела
• мы увидели
• они увидели

So because the subject is мы (we), the verb is plural: увидели.

Not always.

Russian often leaves out subject pronouns when they are clear from context. So depending on context, you could also hear:

• У моря увидели чайку.

But мы is perfectly normal. It can add clarity or emphasis, especially if the speaker wants to make we explicit.

So:

• У моря мы увидели чайку = neutral and clear
• У моря увидели чайку = more context-dependent, with we understood

Russian word order is much more flexible than English word order.

This version puts У моря first to set the scene: By the sea...

Then comes:

• мы — the subject
• увидели — the verb
• чайку — the object

So the sentence flows like: By the sea, we saw a seagull.

Other orders are possible, for example:

• Мы увидели чайку у моря.
• Чайку мы увидели у моря.

These are all grammatical, but the emphasis changes.

Because моря is one of those Russian forms that can be ambiguous by itself.

It can be:

• genitive singular of море
• nominative plural of море

But after у, only the genitive is possible. So here it must mean of the sea / by the sea, not seas.

Not necessarily.

In Russian, чайка often means gull in general. In English, it is often translated as seagull, especially in simple learning materials, because that is the most familiar kind of gull to many learners.

So in context, чайку here is best understood as a gull / a seagull.

A natural stress pattern is:

У мо́ря мы уви́дели ча́йку.

Main word stress:

• мо́ря
• уви́дели
• ча́йку

A rough pronunciation guide:

• у мо́ря ≈ oo MOR-ya
• мы ≈ mɨ (there is no exact English equivalent)
• уви́дели ≈ oo-VEE-dee-lee
• ча́йку ≈ CHAI-koo

The trickiest sound for English speakers is usually ы in мы. It is not the same as English ee.