Мы прошли одну морскую милю.

Прошли is the past tense plural form of пройти.

It tells you:

• the action happened in the past
• the subject is plural
• the verb is perfective, so the action is presented as completed

So прошли here means something like covered / went through / traversed as a finished action.

Yes, мы can sometimes be omitted in Russian if the context is clear.

But here it is useful because прошли only shows plural, not person. By itself, прошли could mean:

• we went / we covered
• they went / they covered

So мы makes it clear that the subject is we.

Because прошли emphasizes a completed distance.

• шли = were going / went, focusing more on the process
• прошли = went through / covered, focusing on reaching or completing that distance

With a specific finished amount such as one nautical mile, прошли is the natural choice.

Not always.

Although пройти often relates to going on foot, it can also mean to cover a distance more generally. In navigation or travel contexts, Russian often uses it for a ship, group, or route as well.

So in this sentence, it does not have to mean literal walking. With морскую милю, it more naturally means we covered one nautical mile.

Because it is the direct object of the verb прошли.

Russian often uses the accusative to show the distance covered with verbs like:

• пройти — cover on foot / traverse
• проехать — cover by vehicle
• пробежать — run
• проплыть — swim / sail

So:

• dictionary form: миля
• accusative singular: милю

The words modifying it must match that case too:

• одну
• морскую

Because один changes like an adjective and must agree with миля.

Миля is:

• feminine
• singular
• accusative here

So the correct form is одну.

Compare:

• nominative masculine: один
• nominative feminine: одна
• accusative feminine: одну

Because the adjective has to agree with милю in:

• gender
• number
• case

The dictionary form is морской.
Here it modifies a feminine singular noun in the accusative, so it becomes морскую.

So the full phrase agrees internally:

• одну — feminine accusative singular
• морскую — feminine accusative singular
• милю — feminine accusative singular

Because one works differently from higher numbers in Russian.

With один / одна / одно, the numeral behaves more like an adjective and agrees with the noun.

So you get:

• одну морскую милю

But with larger numbers, the pattern changes:

• две морские мили
• пять морских миль

That is why you do not see genitive here after one.

No, Russian word order is flexible.

Мы прошли одну морскую милю is the most neutral order.

Other orders are possible, but they change the emphasis:

• Одну морскую милю мы прошли — emphasizes the distance
• Мы одну морскую милю прошли — can sound contrastive or conversational

For learners, the original order is the safest neutral choice.

The main stresses are:

Мы прошлИ однУ морскУю мИлю.

So:

• прошли — stress on the last syllable
• одну — stress on the last syllable
• морскую — stress on -ску́-
• милю — stress on the first syllable

Getting the stress right is important, because Russian stress is not always predictable from spelling.