Мы увидели старую церковь.

Because старую is in the accusative case, feminine singular.

In this sentence, церковь is the direct object of увидели (saw), so the adjective that describes it has to match it in:

• gender: feminine
• number: singular
• case: accusative

So:

• nominative: старая церковь = an/the old church (as the subject)
• accusative: старую церковь = an/the old church (as the object)

That is why старая changes to старую.

For this noun, the accusative singular is the same as the nominative singular.

Церковь is:

• feminine
• inanimate
• singular

For many inanimate nouns in Russian, the accusative looks exactly like the nominative.

So:

• nominative: церковь
• accusative: церковь

The adjective changes visibly (старая → старую), but the noun itself does not change in form here.

Увидели is:

• past tense
• plural
• from the verb увидеть (to see, perfective)

Russian past tense is often formed from the verb stem plus endings that show gender/number:

• увидел = he saw
• увидела = she saw
• увидело = it saw
• увидели = they/we saw

Because the subject is мы (we), the verb takes the plural past form: увидели.

This is about aspect, which is very important in Russian.

• видеть / видели = imperfective
• увидеть / увидели = perfective

Very roughly:

• видели focuses more on the process, repeated action, or general fact of seeing
• увидели focuses on the event as a completed whole: caught sight of / saw

So:

• Мы видели старую церковь. = We saw the old church / We used to see the old church / We were seeing the old church, depending on context
• Мы увидели старую церковь. = We saw (spotted) the old church

In your sentence, увидели suggests a completed event: at some moment, we noticed/saw it.

Russian has no articles like English a/an and the.

So церковь can mean:

• a church
• the church

Which meaning is intended depends on context.

So Мы увидели старую церковь could mean:

• We saw an old church
• We saw the old church

Both are possible unless the wider context makes one interpretation clearer.

Yes, Russian word order is flexible.

The neutral, standard order here is:

• Мы = subject
• увидели = verb
• старую церковь = object

So this is the most straightforward version.

But Russian can rearrange words for emphasis, style, or information focus. For example:

• Старую церковь мы увидели.
  Emphasizes the old church
• Увидели мы старую церковь.
  Can sound more marked, narrative, or contrastive

Because Russian uses case endings, the grammar is still clear even when word order changes.

Sometimes yes, but context matters.

Russian often omits subject pronouns when they are obvious from context. However, in the past tense, the plural form увидели does not by itself tell you whether the subject is:

• we
• they

So:

• Мы увидели старую церковь. = We saw an/the old church
• Увидели старую церковь. = could mean We saw... or They saw..., depending on context

That is why including мы can be useful or necessary.

You usually learn the noun's gender as part of the word.

Церковь is a feminine noun. One clue is that it ends in a soft sign (ь) and belongs to a group of feminine nouns often called the third declension.

Some other feminine nouns of this type are:

• ночь = night
• дверь = door
• площадь = square

Because церковь is feminine, the adjective must also be feminine:

• старая церковь (nominative)
• старую церковь (accusative)

Usually, yes.

Увидеть is a transitive verb, and its direct object normally goes in the accusative:

• увидеть дом = to see a house
• увидеть сестру = to see a sister
• увидеть церковь = to see a church

In your sentence, the direct object is старую церковь, so it appears in the accusative.

One thing to remember: with animate nouns, the accusative form may look different from the nominative. With inanimate nouns like церковь, it often does not.

The stress is:

Мы уви́дели ста́рую це́рковь.

A rough pronunciation guide:

• Мы = mɨ (the Russian ы has no exact English equivalent)
• уви́дели = oo-VEE-dee-lee
• ста́рую = STA-roo-yoo
• це́рковь = TSER-kaf’ or TSER-kov’ depending on how narrowly you describe the pronunciation

A more learner-friendly approximation: mɨ oo-VEE-dee-lee STA-roo-yoo TSER-kof'

Main stresses:

• уви́дели
• ста́рую
• це́рковь

The dictionary forms are:

• мы → мы = we
• увидели → увидеть = to see (perfective)
• старую → старый = old
• церковь → церковь = church

A useful thing to notice is that adjectives are usually listed in dictionaries in the masculine nominative singular form, so старую is looked up as старый.