Jutro obudzę się wcześnie, żeby zdążyć na pociąg.

Because obudzić się is a perfective verb. In Polish, perfective verbs do not normally have a true present tense; their present-looking forms are used for the future.

So:

• obudzę się = I will wake up
• not I am waking up / I wake up

If you wanted a present or habitual meaning, you would use the imperfective verb budzić się, for example Budzę się wcześnie codziennie.

Się is a very common Polish reflexive marker. With obudzić, it changes the meaning from wake someone up to wake up.

Compare:

• obudzić kogoś = to wake someone
• obudzić się = to wake up

So obudzę się means I will wake up. Without się, the sentence would mean something different.

In neutral Polish word order, się often comes after the finite verb or near the beginning of the clause, but it usually does not stand in first position.

So obudzę się is the most natural order here.

You may sometimes see different placement in other sentences, but for a learner, verb + się is a very good default pattern.

Because wcześnie is an adverb, and the sentence needs an adverb to describe how early / at what time the waking happens.

• wczesny is an adjective: wczesny pociąg = an early train
• wcześnie is an adverb: obudzę się wcześnie = I will wake up early

So wcześnie is the correct form because it modifies the verb phrase.

Żeby introduces a purpose clause. It tells you why the speaker will wake up early.

So the structure is:

• obudzę się wcześnie = the main action
• żeby zdążyć na pociąg = the purpose, the reason for doing it

In English, this is often like in order to or so that.

Because the subject of both actions is the same: I will wake up early, and I want to make it in time for the train.

When the subject is the same, Polish very often uses:

• żeby + infinitive

So:

• Jutro obudzę się wcześnie, żeby zdążyć na pociąg.

If the subject were different, Polish would usually use a personal verb form instead, for example:

• Obudzę cię wcześnie, żebyś zdążył na pociąg.
  = I’ll wake you up early so that you can catch the train.

Because zdążyć refers to reaching a result: managing to be in time for something. That is a completed, goal-oriented event, so the perfective verb is natural here.

In this sentence, the speaker wants to wake up early in order to successfully make it for the train. That idea of a completed success fits zdążyć very well.

With zdążyć, Polish usually uses na when talking about being in time for an event, departure, class, meeting, bus, train, and so on.

So you say:

• zdążyć na pociąg
• zdążyć na autobus
• zdążyć na lekcję

This means to make it in time for the train, bus, lesson, etc.

Using do pociągu would suggest movement into the train, not the standard idea of catching / making it for the train. In this context, na pociąg is the normal choice.

Yes. In standard Polish spelling, a clause introduced by żeby is separated with a comma.

So:

• Jutro obudzę się wcześnie, żeby zdążyć na pociąg.

The comma is correct and expected here.

Yes. Polish word order is fairly flexible, and changing it usually changes emphasis, not the basic meaning.

For example:

• Jutro obudzę się wcześnie, żeby zdążyć na pociąg.
• Obudzę się jutro wcześnie, żeby zdążyć na pociąg.

Both are possible, but putting jutro first sounds very natural because it sets the time frame right away: as for tomorrow...

Yes, but the meaning shifts slightly.

• obudzę się wcześnie = I will wake up early
• wstanę wcześnie = I will get up early

In real life, these can both fit the situation, but they are not identical. Obudzić się focuses on the moment of waking up; wstać focuses more on getting out of bed / getting up.