Мы перешли через деревянный мостик и пошли дальше к воде.

Because the subject is мы (we). In Russian past tense, verbs agree with the subject in number and, in the singular, also gender.

• я пошёл / я пошла = I went
• он пошёл = he went
• она пошла = she went
• мы пошли = we went

So:

• мы перешли = we crossed
• мы пошли = we went / started walking

Both verbs are plural because мы is plural.

They describe two different actions in sequence.

• перешли = crossed
• пошли дальше = went on / continued walking

So the sentence breaks down like this:

1. Мы перешли через деревянный мостик = We crossed the wooden footbridge.
2. и пошли дальше к воде = and then went farther toward the water.

Russian often uses separate motion verbs very precisely, where English might be a little looser.

They are perfective because the sentence presents the actions as completed, single events in a narrative.

• перейти (perfective) = to cross, to get across
• пойти (perfective) = to set off, to start going

In this sentence, the speaker is telling what happened next:

• first, we crossed
• then, we went on

That is why perfective verbs are natural here.

If you used imperfective forms, the focus would be different:

• переходили = were crossing / used to cross
• шли = were going / walking

Those would sound more like process or background, not a completed sequence of events.

This is a very common question.

• шли = were going / went (as a process)
• пошли = started going / set off / went on

So пошли дальше suggests a new step in the story: after crossing the bridge, they continued onward.

Compare:

• Мы шли к воде. = We were walking toward the water.
• Мы пошли к воде. = We started walking toward the water / we headed toward the water.

In your sentence, пошли дальше fits the idea of moving on after finishing the first action.

The preposition через usually takes the accusative case.

So:

• через мостик = across the little bridge / over the footbridge

Here, мостик is a masculine inanimate noun. In the accusative singular, masculine inanimate nouns usually look the same as the nominative:

• nominative: деревянный мостик
• accusative: деревянный мостик

That is why the form does not visibly change.

Because it agrees with мостик, and in this sentence the noun is masculine singular inanimate accusative.

For masculine inanimate nouns, the accusative usually has the same form as the nominative, and the adjective matches that:

• nominative: деревянный мостик
• accusative: деревянный мостик

If the noun were animate, the form would often change differently. But мостик is inanimate, so деревянный stays деревянный.

Мостик is a diminutive form of мост.

• мост = bridge
• мостик = little bridge, small bridge, footbridge

A diminutive can suggest:

• small size
• something quaint or light
• sometimes a warmer, more descriptive tone

In this sentence, деревянный мостик gives the image of a small wooden bridge or footbridge, not a large bridge.

Because the preposition к requires the dative case.

The noun вода changes like this:

• nominative: вода
• dative: воде

So:

• к воде = toward the water / to the water

This is one of the basic preposition-case pairings to remember:

• к + dative

Russian has no articles like a or the. So вода can mean:

• water
• the water

The exact meaning depends on context.

In this sentence, к воде is naturally understood as toward the water, probably a specific body of water nearby, because the setting makes it clear. Russian relies on context rather than articles.

Дальше means farther, further, or onward, depending on context.

In пошли дальше к воде, it means something like:

• went farther toward the water
• continued on toward the water

It shows that after crossing the bridge, they did not stop—they kept going.

Yes, that is also possible.

Russian allows both patterns:

• перейти мостик / мост = to cross the bridge
• перейти через мостик / через мост = to go across the bridge

With через, the idea of crossing across/over is more explicit. Without it, the verb перейти itself already carries the idea of crossing.

Both are natural, though the version with через is very common.

Yes, Russian word order is flexible. The given order is a neutral, natural narrative order:

• subject first: Мы
• first action: перешли через деревянный мостик
• second action: и пошли дальше к воде

You could change the word order for emphasis, for example:

• Через деревянный мостик мы перешли и пошли дальше к воде.

But that would shift the focus slightly. The original version sounds like normal storytelling.

Yes. Russian often drops subject pronouns when the verb form already makes the subject clear.

So you could say:

• Перешли через деревянный мостик и пошли дальше к воде.

That can still mean We crossed the wooden footbridge and went farther toward the water, depending on context.

Including мы makes the subject explicit. It may sound slightly clearer, more deliberate, or more contrastive, depending on context.