Dobrze, że wcześniej udało mi się zarezerwować miejsca, bo dziś jest dużo ludzi.

Yes. Dobrze, że... means It’s good that... or It’s a good thing that....

In full, the sentence starts with the idea:

Dobrze, że wcześniej udało mi się...
= It’s good that I managed earlier to...

Polish often leaves out to in this kind of sentence, so although you can also hear To dobrze, że..., the shorter Dobrze, że... is very natural.

Udało mi się means something like:

• I managed to
• I succeeded in
• I was able to
• sometimes even I was lucky enough to

It comes from the verb udać się, which is a very common expression in Polish.

So:

• udało mi się zarezerwować miejsca
  = I managed to reserve seats

A useful thing to notice is that this expression sounds a bit less direct than plain English I did it. It often suggests that the result was successfully achieved, sometimes with a hint of relief or luck.

Mi is the unstressed dative form of ja (to me), and it is the normal form in a sentence like this:

• udało mi się = it worked out for me / I managed

Mnie is the stressed form, used for emphasis, contrast, or after some prepositions.

Compare:

• Udało mi się. = I managed.
• Mnie się udało, a jemu nie. = I managed, but he didn’t.

So in your sentence, mi is the natural choice.

In udać się, się is part of the verb expression. You should learn udać się as a whole unit.

So:

• udać się = to succeed / to work out
• udało mi się = I managed / it worked out for me

Even though się often looks like oneself, here it is not really translated word-for-word into English. It is just part of how this verb works.

Because udało się is an impersonal construction.

Literally, it works more like:

• It succeeded for me
• It worked out for me

That is why you get udało in the neuter singular form, instead of a past-tense form agreeing with the speaker’s gender.

So:

• udało mi się zarezerwować miejsca
  literally resembles it worked out for me to reserve seats
• natural English: I managed to reserve seats

This is one of the most important things to understand about udało mi się: grammatically, Polish is not saying I managed in the same direct way English does.

Because after udało mi się, Polish commonly uses an infinitive to say what someone managed to do.

So:

• udało mi się zarezerwować miejsca
  = I managed to reserve seats

The infinitive is zarezerwować because this is a completed action: the reservation was successfully made.

This is the perfective verb. The imperfective partner is rezerwować.

Compare:

• rezerwować = to be reserving / to reserve in a general, repeated, or ongoing sense
• zarezerwować = to reserve successfully / to make a reservation as a completed action

Since the sentence talks about a successful completed result, zarezerwować is the right choice.

Miejsca is the accusative plural of miejsce (place, seat, spot).

Here it means seats or places in the sense of reserved spots.

The verb zarezerwować takes a direct object, so we need the accusative:

• zarezerwować co? → miejsca

For this noun, the nominative plural and accusative plural look the same:

• nominative plural: miejsca
• accusative plural: miejsca

So even though the form looks unchanged, the function is accusative here.

Yes, it can move.

Wcześniej means earlier or beforehand, and Polish word order is quite flexible. In your sentence, putting it early helps emphasize that the reservation happened in advance.

You could also say:

• Dobrze, że udało mi się wcześniej zarezerwować miejsca...

This is also natural.

The difference is mainly emphasis:

• że wcześniej udało mi się... → emphasis on earlier / in advance
• że udało mi się wcześniej zarezerwować... → a bit more neutral, with earlier attached more closely to the action

Both are correct.

Yes, ponieważ is possible, but bo is more common in everyday speech.

• bo = because
• ponieważ = because / since, but a bit more formal or written

So:

• ..., bo dziś jest dużo ludzi. = natural, conversational
• ..., ponieważ dziś jest dużo ludzi. = also correct, but slightly more formal

In ordinary spoken Polish, bo is extremely common.

There are two important things here.

1. Why dużo ludzi?

After dużo (a lot of), Polish usually uses the genitive:

• dużo ludzi = a lot of people

The noun ludzie has the genitive plural form ludzi.

2. Why jest and not są?

With expressions like dużo, mało, wiele, Polish very often uses a singular neuter-style verb in existential sentences:

• Jest dużo ludzi. = There are a lot of people.

So even though English says there are, Polish often says jest in this structure.

That is why jest dużo ludzi is correct and natural.

They are different case forms of the same word.

• ludzie = nominative plural = people
• ludzi = genitive plural (also accusative in some contexts)

In this sentence, we need ludzi because it follows dużo:

• dużo ludzi = a lot of people

You would use ludzie when the noun is the subject in the basic nominative form:

• Ludzie czekają. = People are waiting.

Because Polish punctuation normally requires commas before conjunctions that introduce subordinate clauses, including że and bo.

So:

• Dobrze, że...
• ..., bo...

Both commas are standard and necessary in normal written Polish.

This is one area where Polish is often more strict than English.

Yes. Miejsce literally means place, but in many contexts it naturally means:

• seat
• spot
• space
• place

So zarezerwować miejsca can mean:

• reserve seats
• reserve places/spots

The exact English translation depends on context. If this is about a train, cinema, theater, or restaurant, seats is often the most natural translation.

It is neutral and very natural.

Nothing in it is especially slangy or especially formal. It sounds like normal everyday Polish.

A native speaker could say it in conversation without any problem:

• Dobrze, że wcześniej udało mi się zarezerwować miejsca, bo dziś jest dużo ludzi.

If you replaced bo with ponieważ, it would sound a bit more formal, but the original sentence is completely standard.

Yes, but it is not exactly the same.

• Dobrze, że wcześniej udało mi się zarezerwować miejsca
  emphasizes that you managed to do it successfully
• Dobrze, że zarezerwowałem miejsca wcześniej
  simply says It’s good that I reserved the seats earlier

So the original sentence includes the idea of success / managing to do it, while your version just states the action more directly.

That makes udało mi się slightly more expressive, especially if it might have been difficult to get the reservation.