Ontem tivemos um problema com um pneu na estrada, mas felizmente uma vizinha deu-nos boleia até casa.

Because this sentence is describing completed events in the past.

• tivemos = we had
• deu = she gave

These are both in the pretérito perfeito simples, which is the normal tense in Portuguese for finished actions or events.

So:

• Ontem tivemos um problema... = Yesterday we had a problem...
• uma vizinha deu-nos boleia... = a neighbour gave us a lift...

If you used the imperfect instead:

• tínhamos
• dava

it would sound more like background, habit, or an ongoing situation, not a single completed event.

Very often, yes. Ontem means yesterday, so it usually points to a specific finished time in the past. That makes the pretérito perfeito the natural choice.

Examples:

• Ontem choveu. = It rained yesterday.
• Ontem fui ao supermercado. = I went to the supermarket yesterday.
• Ontem tivemos um problema. = Yesterday we had a problem.

You do not use this tense only because of ontem, but ontem strongly suggests a finished past event, so this tense is very common with it.

Literally, it means a problem with a tyre.

In real life, this usually implies something like:

• a flat tyre
• a puncture
• some other tyre-related problem

Portuguese often leaves this a bit unspecific if the exact issue is not important. So tivemos um problema com um pneu is a very natural way to say that something went wrong with one of the tyres.

A more specific version could be:

• O pneu furou. = The tyre got punctured / went flat.

But the sentence you were given is more general.

Because na is a contraction.

• em = in / on / at
• a = the for a feminine singular noun
• em + a = na

So:

• na estrada = on the road

This kind of contraction is extremely common in Portuguese:

• em + o = no
• em + a = na
• em + os = nos
• em + as = nas

Since estrada is feminine, you get na estrada.

Because uma vizinha means a neighbour, while a vizinha means the neighbour.

The indefinite article uma is used when the person is being introduced as new information, or when it does not matter exactly which neighbour she is.

So:

• uma vizinha = a neighbour
• a vizinha = the neighbour

If the speaker and listener both already knew which neighbour was being talked about, a vizinha would make more sense.

Yes. Vizinha is specifically a female neighbour.

• vizinho = male neighbour
• vizinha = female neighbour

Portuguese nouns and adjectives often show gender this way.

So in this sentence, the person who helped was a woman.

This is a very common European Portuguese question.

In Portugal Portuguese, object pronouns often come after the verb in affirmative main clauses. This is called enclisis.

So:

• deu-nos boleia = gave us a lift

Here:

• deu = gave
• nos = to us / us

In Brazilian Portuguese, nos deu is more common in normal speech. But in European Portuguese, deu-nos is the standard pattern here.

So for Portugal Portuguese, this sentence is exactly what you would expect.

Here nos means to us or us.

The verb phrase is:

• dar boleia a alguém = to give someone a lift

So:

• deu-nos boleia = she gave us a lift

Literally, it is something like:

• gave-us a lift

Portuguese often uses these short object pronouns:

• me = me / to me
• te = you / to you
• lhe = him, her / to him, to her
• nos = us / to us
• vos = you plural / to you plural
• lhes = them / to them

Yes. In European Portuguese, boleia is the normal word for a lift or a ride in someone else’s vehicle.

The common expression is:

• dar boleia = to give someone a lift
• pedir boleia = to ask for a lift
• apanhar boleia = to get a lift / hitch a ride

This is a very useful everyday word in Portugal.

A learner should also know that in Brazilian Portuguese, people more often say carona instead of boleia.

So:

• Portugal: dar boleia
• Brazil: dar carona

Because casa often appears without an article when it means home.

So:

• até casa = as far as home / home
• ir para casa = to go home
• chegar a casa = to arrive home
• estar em casa = to be at home

This is similar to English, where we usually say go home, not go to the home.

But a casa can appear when you mean the house in a more literal, specific sense.

Compare:

• Fomos até casa. = We went home.
• Fomos até à casa da Ana. = We went as far as Ana’s house.

So in your sentence, até casa means home, not just to the house.

It connects the bad event with the positive outcome.

• mas = but
• felizmente = fortunately

So the sentence first gives the problem:

• Ontem tivemos um problema com um pneu na estrada...

and then introduces the good result:

• mas felizmente uma vizinha deu-nos boleia até casa.

Felizmente is an adverb, and it can often move around a little:

• mas felizmente uma vizinha deu-nos boleia...
• mas uma vizinha felizmente deu-nos boleia...
• felizmente, uma vizinha deu-nos boleia...

The version in your sentence sounds natural and clear.

Yes, but it is usually not necessary.

Portuguese often leaves out subject pronouns because the verb ending already shows who the subject is.

• tivemos already tells you it means we had

So:

• Ontem tivemos um problema... = natural
• Ontem nós tivemos um problema... = also possible, but more emphatic

You might add nós if you want contrast or emphasis, for example:

• Eles não tiveram problemas, mas nós tivemos.

In the original sentence, leaving out nós is the most natural choice.

It is clearly European Portuguese.

The biggest clues are:

• deu-nos instead of the more Brazilian nos deu
• boleia instead of the more Brazilian carona

A Brazilian version would more likely be something like:

• Ontem tivemos um problema com um pneu na estrada, mas felizmente uma vizinha nos deu carona até em casa
  or more naturally
• ...nos deu carona até em casa / até nossa casa / para casa, depending on context

So the original sentence is a very good model for Portugal Portuguese.