Nasz pociąg odjeżdża z peronu drugiego.

Because pociąg is a masculine singular noun, and nasz has to agree with it in gender, number, and case.

So in the nominative singular:

• nasz pociąg = our train
• nasza książka = our book
• nasze okno = our window

Here, pociąg is masculine, so nasz is the correct form.

Polish often uses the present tense for scheduled future events, just like English can do in sentences such as Our train leaves at 6:10.

So:

• Nasz pociąg odjeżdża... = Our train is departing / leaves ...
• It sounds natural for timetables, announcements, and fixed plans.

This verb is from odjeżdżać (imperfective), and in this context the present tense refers to a planned future event.

Odjeżdża means departs, especially for a vehicle such as a train, bus, or tram leaving a place.

It comes from odjeżdżać, which suggests movement away from a point of departure.

For example:

• Pociąg odjeżdża o szóstej. = The train departs at six.
• Autobus odjeżdża z przystanku. = The bus leaves from the stop.

It is more specific than a general verb like wyjeżdża in this railway context. Odjeżdżać is the standard verb for transport departures.

After z meaning from, Polish uses the genitive case.

So:

• peron = platform (dictionary form, nominative)
• z peronu = from the platform (genitive)

This is why peron changes to peronu.

A useful thing to remember is that z can mean two different things:

• z + genitive = from
• z + instrumental = with

Compare:

• z peronu = from the platform
• z kolegą = with a friend

In your sentence, it clearly means from, so the genitive is required.

Because drugiego is the genitive singular masculine form of the ordinal number drugi (second), and it agrees with peronu.

Here is the pattern:

• drugi peron = the second platform / platform two
• z drugiego peronu = from the second platform

In your sentence, the wording is z peronu drugiego, but the grammar is the same: drugiego must match the genitive masculine singular form required by peronu.

Why not dwa?

• dwa is a cardinal number: two
• drugi is an ordinal number: second

Platform numbers in this kind of phrase are normally expressed with the ordinal form.

Both are possible, but they sound a little different in style.

• z drugiego peronu is the more everyday, neutral order
• z peronu drugiego sounds more formal, official, or like a station announcement

So the sentence you were given has a slightly official or railway-style feel.

In ordinary conversation, many speakers would probably say:

• Nasz pociąg odjeżdża z drugiego peronu.

But z peronu drugiego is still perfectly correct.

Yes, mainly in aspect and style.

• odjeżdża = imperfective present; often used for schedules and announcements
• odjedzie = perfective future; means will depart

So:

• Nasz pociąg odjeżdża z peronu drugiego. = Our train departs / is departing from platform 2.
• Nasz pociąg odjedzie z drugiego peronu. = Our train will depart from platform 2.

Both can be correct, but odjeżdża is especially natural for fixed timetable information.

Yes, literally it means our train, but in real use it often just means the train we are taking or the train relevant to us.

So a speaker might say:

• Nasz pociąg już stoi na peronie. = Our train is already at the platform.

This does not mean they own the train. It just means it is their train in the practical sense.

A rough pronunciation guide:

• pociąg ≈ PO-chyongk
• odjeżdża ≈ od-YEZH-jah

A few pronunciation notes:

• ci before a vowel often sounds like a soft ch / ć-like sound
• ą is a nasal vowel; before some consonants it may sound a bit like ong/on
• żdż in odjeżdża is a cluster that can be hard at first; try saying it slowly: o-d-je-ż-dża

You do not need perfect pronunciation immediately, but it helps to recognize that Polish spelling is quite regular once you learn the sound patterns.