Перед уходом я подмету пол в прихожей.

Because перед normally takes the instrumental when it means before or in front of.

So:

• уход = departure / leaving
• перед уходом = before leaving / before the departure

This is a very common pattern:

• перед сном = before sleep / before going to bed
• перед работой = before work
• перед встречей = before the meeting

So the case here is controlled by the preposition перед.

Russian often uses a noun phrase where English would use a clause.

So instead of saying something like before I leave, Russian can say:

• перед уходом = literally before departure / before leaving

This is compact and very natural.

A more clause-like version is also possible:

• Перед тем, как я уйду, я подмету пол в прихожей.

That means almost the same thing, but it is longer and a bit more explicit. In everyday speech, перед уходом is often the simpler, more natural choice.

This is a question of aspect.

• подмести is perfective
• подметать is imperfective

подмету is the future form of the perfective verb подмести, and it means a single completed action:

• I will sweep the floor and the action will be finished.

That fits this sentence well, because the speaker means they will do that task before leaving.

If you said буду подметать, that would be imperfective future and would focus more on the process, repetition, or ongoing action. It would sound less natural here unless you specifically wanted to emphasize the activity rather than the completed result.

It comes from подмести, which means to sweep.

This verb changes its stem in the future forms, so it can look surprising at first:

• я подмету
• ты подметёшь
• он/она подметёт
• мы подметём
• вы подметёте
• они подметут

So yes, подмету really is the correct form, even though it looks a bit irregular compared with the infinitive подмести.

The stress is:

• подмету́

It is in the accusative.

The reason it looks unchanged is that for many inanimate masculine singular nouns, the accusative has the same form as the nominative.

So:

• nominative: пол = floor
• accusative: пол = floor

Since пол is masculine singular and inanimate, the accusative form is identical.

Compare:

• Я вижу стол. = I see the table.
  (стол stays the same)
• Я вижу брата. = I see my brother.
  Here the accusative changes because брат is animate.

Because this sentence describes location, not motion toward a destination.

Russian uses:

• в + prepositional for where
• в + accusative for where to

Here, the sweeping happens in the hallway, so we use location:

• в прихожей = in the hallway

Compare:

• Я стою в прихожей. = I am standing in the hallway.
• Я иду в прихожую. = I am going into the hallway.

So в прихожей is correct because the speaker is talking about where the floor is being swept.

Прихожая means entryway, hallway, or entrance hall in a home.

It is the area near the door where people come in, take off shoes, hang coats, and so on.

In this sentence:

• в прихожей = in the hallway / in the entryway

The exact English word depends on the house or apartment layout, but entryway or hallway is usually a good match.

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

The sentence as given is neutral and natural:

• Перед уходом я подмету пол в прихожей.

But other orders are possible, depending on emphasis:

• Я подмету пол в прихожей перед уходом.
• Пол в прихожей я подмету перед уходом.
• В прихожей я подмету пол перед уходом.

These all keep roughly the same basic meaning, but they shift the focus slightly:

• starting with перед уходом emphasizes the time
• starting with я emphasizes the subject
• starting with пол в прихожей emphasizes what exactly will be swept

Usually it means before leaving, but not necessarily at the very last second.

It simply places the action earlier than the departure. The exact timing depends on context.

So it could mean:

• just before leaving
• sometime before heading out
• before the speaker goes away

If you really wanted to stress right before leaving, you would usually rely on context or add another word.

Because Russian has no articles.

There is no separate word corresponding directly to English a or the.

So:

• пол can mean a floor or the floor
• в прихожей can mean in a hallway or in the hallway

Context tells you which one is meant. In this sentence, the most natural English translation is probably the floor in the hallway, because the speaker is likely talking about a specific home and a specific hallway.

Yes, but the meaning would change.

• подмести = to sweep
• помыть пол = to wash / mop the floor
• пропылесосить = to vacuum
• убрать в прихожей = to tidy up / clean the hallway in a general sense

So подмету пол specifically means the speaker will sweep the floor, probably with a broom or something similar.

If the intention were broader, Russian would use a different verb.