Meni je svejedno hoćemo li ići autobusom ili vlakom, samo da stignemo na vrijeme.

Because meni is the dative form of ja.

In Croatian, the expression (nekome) je svejedno means someone doesn’t mind / it’s all the same to someone. So the person affected is put in the dative:

• Meni je svejedno = I don’t mind
• literally: To me, it is all the same

So ja would not work here, because ja is nominative, and this expression requires dative.

Also, in everyday speech, you will very often hear the unstressed form:

• Mi je svejedno.

That means the same as Meni je svejedno, but meni is more emphatic.

Svejedno literally suggests all the same, and in this sentence it means:

• I don’t mind
• It makes no difference to me
• Either is fine with me

So:

• Meni je svejedno hoćemo li ići autobusom ili vlakom
  = I don’t mind whether we go by bus or by train

You can also use svejedno in other ways, for example:

• Svejedno je. = It doesn’t matter.
• Svejedno mi je. = I don’t care / I don’t mind.

Because svejedno here behaves like an impersonal predicate, not like a normal adjective describing I.

Croatian often uses structures like:

• Meni je drago = I am glad
• Meni je žao = I am sorry
• Meni je svejedno = I don’t mind

So the verb is je because the core idea is something like:

• It is all the same to me

It is not literally saying I am all-the-same.

Here hoćemo li means whether we will.

It comes from:

• hoćemo = we will / we want
• li = a question particle

Together, hoćemo li often means shall we? / will we? in a direct question:

• Hoćemo li ići? = Shall we go?

But after another phrase, it can introduce an indirect yes/no question:

• Ne znam hoćemo li ići. = I don’t know whether we will go.
• Meni je svejedno hoćemo li ići autobusom ili vlakom. = I don’t mind whether we go by bus or by train.

So here it is not a direct question, but an embedded whether clause.

This is the normal way to form the Croatian future tense:

• present tense of htjeti
  • infinitive

So:

• hoćemo ići = we will go
• hoćemo li ići = whether we will go / will we go?

The verb ići stays in the infinitive because it is part of the future construction.

A few examples:

• Ići ćemo sutra. = We will go tomorrow.
• Hoćemo li ići sutra? = Will we go tomorrow?
• Ne znam hoćemo li ići sutra. = I don’t know whether we will go tomorrow.

Yes, you could.

Both can mean whether we will go:

• hoćemo li ići
• da li ćemo ići

But hoćemo li is often felt to be a bit more natural or elegant in many contexts, especially in standard language.

So these are both possible:

• Meni je svejedno hoćemo li ići autobusom ili vlakom.
• Meni je svejedno da li ćemo ići autobusom ili vlakom.

The first version is very natural and compact.

Because they are in the instrumental case.

In Croatian, means of transport are often expressed with the instrumental, usually without a preposition:

• autobusom = by bus
• vlakom = by train
• autom = by car
• brodom = by ship
• avionom = by plane

So:

• ići autobusom = to go by bus
• ići vlakom = to go by train

This instrumental often answers the question How? By what means?

Because Croatian often uses the instrumental alone for means of transport.

In English you need by:

• by bus
• by train

But in Croatian, the case itself already carries that function:

• autobusom
• vlakom

So no extra preposition is needed.

This is very common:

• Idem tramvajem. = I’m going by tram.
• Putujemo autom. = We’re travelling by car.

Here samo da means something like:

• as long as
• provided that
• the important thing is that
• just so that

So:

• samo da stignemo na vrijeme
  = as long as we arrive on time

It expresses the speaker’s real priority. The person does not care about the bus/train choice; the only important thing is arriving on time.

This is a very common Croatian structure.

Examples:

• Svejedno mi je gdje ćemo jesti, samo da nije preskupo.
  = I don’t mind where we eat, as long as it isn’t too expensive.

• Idi kako hoćeš, samo da dođeš na vrijeme.
  = Go however you want, as long as you arrive on time.

Because after da, Croatian often uses a present-tense form to express a future result, wish, goal, or condition.

Here:

• samo da stignemo na vrijeme

literally looks like present tense, but it refers to a future event: that we arrive on time.

Also, stignemo comes from the verb stići, which is perfective. In Croatian, perfective present forms often refer to future completion when used in clauses like this.

So stignemo here naturally means:

• we arrive / we manage to arrive
  with future meaning in context.

You generally would not say:

• samo da ćemo stići na vrijeme

in this sentence. The da + present structure is the normal one.

Stići means to arrive / to make it / to get there in time, often with an idea of successful arrival.

Doći simply means to come / to arrive, but stići is especially natural when timing matters.

So:

• stignuti na vrijeme = to arrive on time / to make it in time

That is why it fits perfectly here.

Compare:

• Došli smo u Zagreb. = We arrived in Zagreb.
• Jedva smo stigli na vrijeme. = We barely made it on time.

Since the sentence is about not caring how we travel, as long as timing is okay, stići na vrijeme is the best choice.

Na vrijeme means:

• on time
• in time

In many situations, English distinguishes those two, but Croatian often uses na vrijeme for both.

Examples:

• Došao je na vrijeme. = He arrived on time.
• Moramo stići na vrijeme. = We have to get there on time / in time.

It is a fixed expression, so it is best learned as a whole phrase.

Because samo da stignemo na vrijeme is a separate subordinate clause that adds the condition or priority.

The sentence has two main parts:

• Meni je svejedno hoćemo li ići autobusom ili vlakom
• samo da stignemo na vrijeme

The comma helps separate the main idea from the added condition:

• I don’t mind whether we go by bus or by train, as long as we arrive on time.

This punctuation is normal and natural.

Yes, Croatian word order is fairly flexible, though some versions sound more natural than others.

The given sentence is very natural:

• Meni je svejedno hoćemo li ići autobusom ili vlakom, samo da stignemo na vrijeme.

You might also hear:

• Svejedno mi je hoćemo li ići autobusom ili vlakom, samo da stignemo na vrijeme.

That is probably the most common conversational version, using the unstressed mi instead of meni.

Using meni at the start gives a little more emphasis, like:

• As for me, I don’t mind...

So the original wording is correct and natural, just slightly more emphatic.

Yes, pretty much.

Here:

• autobusom ili vlakom = by bus or by train

It presents two alternatives.

Croatian can also repeat ili for extra emphasis, similar to English either ... or ...:

• ili autobusom ili vlakom

But in your sentence, a single ili is perfectly normal and natural.

A very natural casual version would be:

• Svejedno mi je hoćemo li ići autobusom ili vlakom, samo da stignemo na vrijeme.

This differs from the original only in using mi instead of meni and putting svejedno first.

You might also hear:

• Svejedno mi je idemo li autobusom ili vlakom, samo da stignemo na vrijeme.

That version uses idemo li instead of hoćemo li ići, which can sound a bit more direct and conversational in some contexts.

All of these are normal; the original sentence is absolutely correct and idiomatic.