No me da igual que el tren llegue con retraso.

Dar igual is an idiomatic expression meaning to make no difference, to be all the same, or not to matter.

So:

• Me da igual... = I don’t mind... / It makes no difference to me...
• No me da igual... = I do mind... / It does matter to me...

You should not try to translate dar literally here as to give. The whole expression works as one unit.

Me is an indirect object pronoun, and it shows to whom something matters or makes no difference.

So:

• me da igual = it makes no difference to me
• te da igual = it makes no difference to you
• le da igual = it makes no difference to him / her / you (formal)

In this sentence, me tells us that the speaker is the person affected.

Because the speaker is negating the expression me da igual.

• Me da igual que el tren llegue con retraso = I don’t mind if the train is late
• No me da igual que el tren llegue con retraso = I do mind if the train is late

So yes, adding no here changes the meaning to the opposite.

Because after expressions like me da igual que, Spanish normally uses que + subjunctive.

This is a very common pattern when the main clause expresses an attitude, reaction, judgment, or emotional stance toward a situation:

• Me molesta que llegue tarde
• Me gusta que vengas
• Me da igual que llueva
• No me da igual que el tren llegue con retraso

So llegue is the present subjunctive of llegar.

Yes.

Both of these use the subjunctive:

• Me da igual que el tren llegue con retraso
• No me da igual que el tren llegue con retraso

The negation changes the meaning, but it does not change the fact that dar igual que is followed by the subjunctive.

Que introduces the subordinate clause: que el tren llegue con retraso.

In English, this often corresponds to that or is left untranslated:

• No me da igual que el tren llegue con retraso
• It does matter to me that the train is late
• I do mind that the train is arriving late

In Spanish, que is normally required in this structure.

Con retraso is a very common way to talk about transport being delayed, especially trains, planes, and buses.

• El tren llega con retraso = the train arrives delayed / is running late

You can also say llegar tarde, but con retraso sounds especially natural for transport and scheduled services.

Very roughly:

• llegar tarde = arrive late
• llegar con retraso = arrive with a delay / be delayed

In Spain, con retraso is extremely common in travel contexts.

Yes, it is natural and understandable.

That said, No me da igual... is a bit less common than the positive Me da igual..., simply because people more often say they don’t mind something than explicitly negate it.

Depending on the exact nuance, a speaker might also say:

• Me importa que el tren llegue con retraso = It matters to me that the train is late
• Me molesta que el tren llegue con retraso = It bothers me that the train is late
• No me da lo mismo que el tren llegue con retraso = It’s not all the same to me that the train is late

But your original sentence is perfectly valid.

Yes, Spanish word order is somewhat flexible.

The most neutral version is:

• No me da igual que el tren llegue con retraso

But you could also move the subordinate clause for emphasis:

• Que el tren llegue con retraso no me da igual

That version sounds more emphatic, as if the speaker wants to highlight the train being late.

Not in this meaning.

To say it makes no difference to me, Spanish normally uses the expression dar igual, not ser igual.

So the natural forms are:

• Me da igual
• No me da igual

Not:

• Me es igual in this context

You may hear me es igual occasionally, but me da igual is much more standard and common in everyday Spanish.