Hvis vi løber tør for benzin, må vi finde en tankstation.

Hvis means if and introduces a conditional clause.

So Hvis vi løber tør for benzin is the if-clause: it sets up the condition under which the rest of the sentence becomes relevant.

This works very much like English:

• Hvis det regner, bliver vi hjemme.
• If it rains, we stay home.

So in your sentence, Hvis tells you right away that the first part is not the main statement, but the condition for it.

Yes — løbe tør for is a very common fixed expression meaning to run out of.

It breaks down like this:

• løber = run/runs (present tense of løbe)
• tør = literally dry
• for = of/for

But you should learn løbe tør for as a whole unit, because its meaning is idiomatic. It does not mean physical running here.

Examples:

• Vi løber tør for mælk. = We run out of milk.
• Hun løb tør for penge. = She ran out of money.
• Bilen er løbet tør for benzin. = The car has run out of petrol/gas.

So in this sentence, løber tør for benzin is best understood as one chunk: run out of petrol.

Because løber is the present tense form, and this clause needs a finite verb.

The subject is vi, so Danish uses the present tense:

• jeg løber
• du løber
• vi løber

Unlike English, Danish does not change the present tense verb for different persons very much. The same form is used for all subjects.

So:

• vi løber tør for benzin = we run out of petrol / we are running out of petrol

You would use løbe only as the infinitive, for example:

• at løbe = to run
• Vi kan løbe. = We can run.

This is because Danish main clauses follow the verb-second rule.

The first element in the full sentence is the subordinate clause:

• Hvis vi løber tør for benzin

After that, the main clause begins, and in a Danish main clause the finite verb usually comes in second position. So you get:

• må vi finde en tankstation

not

• vi må finde en tankstation

The structure is:

1. Hvis vi løber tør for benzin
2. må
3. vi
4. finde en tankstation

Compare:

• Vi må finde en tankstation.
• Hvis vi løber tør for benzin, må vi finde en tankstation.

When the if-clause comes first, it takes the first slot, so the verb in the main clause comes before the subject.

Here må means must or have to.

In this sentence, it expresses necessity:

• må vi finde en tankstation = we must / have to find a gas station

This can be confusing because må can have other meanings in other contexts, including something closer to may.

For example:

• Må jeg gå nu? = May I go now?
• Det må være rigtigt. = That must be right.

So må is a modal verb with several uses. In your sentence, the context clearly gives the meaning must/have to.

Because after a modal verb in Danish, the next verb normally appears in the bare infinitive — without at.

So:

• må finde
• kan finde
• skal finde
• vil finde

not:

• må at finde

Examples:

• Jeg kan svømme. = I can swim.
• Vi skal gå. = We have to go.
• Hun vil købe en bil. = She wants to buy a car.

So in your sentence:

• må vi finde en tankstation

is correct because finde follows the modal verb må directly.

Because the sentence begins with a subordinate clause, and the comma marks the boundary between that clause and the main clause.

So:

• Hvis vi løber tør for benzin, må vi finde en tankstation.

The comma shows that the if-clause has ended and the main clause is starting.

This is very common in Danish when a subordinate clause comes first.

Because the sentence means a gas station, not the gas station.

• en tankstation = a gas station
• tankstationen = the gas station

Here, the speaker is not referring to one specific, already known station. They just mean that they need to find some gas station.

Compare:

• Vi må finde en tankstation. = We need to find a gas station.
• Vi må finde tankstationen. = We need to find the gas station.

So the indefinite form is the natural choice here.

Because løbe tør for is the fixed pattern, and for is part of that expression.

You cannot usually swap it out freely. With this idiom, Danish uses:

• løbe tør for noget = run out of something

Examples:

• løbe tør for kaffe
• løbe tør for tid
• løbe tør for strøm

So for is not being chosen independently here in the way an English learner might expect. It belongs to the whole phrase.

Yes. Benzin in Danish means petrol/gasoline.

A useful note for English speakers:

• British English: petrol
• American English: gas or gasoline
• Danish: benzin

So tankstation is a place where you buy benzin.

Yes. You could say:

• Vi må finde en tankstation, hvis vi løber tør for benzin.

That is also correct.

The difference is mostly in emphasis and word order:

• Hvis vi løber tør for benzin, må vi finde en tankstation.
  The condition comes first.

• Vi må finde en tankstation, hvis vi løber tør for benzin.
  The main statement comes first.

Notice that when the main clause comes first, the normal order is:

• Vi må finde ...

But when the if-clause comes first, the main clause changes to:

• må vi finde ...

because of the Danish verb-second rule.