Мне повезло с квартирой.

Because Russian uses a different structure here from English.

In Мне повезло с квартирой, the person who experiences the luck is put in the dative case: мне = to me.

A very literal way to think of the sentence is:

To me, it turned out luckily with the apartment.

So Russian is not treating I as a normal subject here. This is a common pattern with impersonal expressions:

• Мне повезло. = I got lucky.
• Мне холодно. = I am cold.
• Мне интересно. = I am interested / It is interesting to me.

So мне is exactly what Russian expects in this construction.

Повезло is the past-tense form of повезти, meaning to be lucky for someone / to turn out luckily for someone.

In this sentence, it means something like:

• I got lucky
• Things worked out well for me
• I was fortunate

It is an impersonal form, which is why it does not agree with квартира.

This is an important point: повезло does not mean the apartment was lucky. It means luck happened to me in connection with the apartment.

Because this is an impersonal past-tense construction.

In Russian, impersonal past expressions often appear in the neuter singular form:

• Мне повезло.
• Мне не спалось.
• Нам удалось.

The -ло ending is the neuter past ending. It does not mean that the sentence is talking about some neuter noun. It is just the standard form Russian often uses when there is no normal grammatical subject.

So the verb is not agreeing with квартирой.

Квартирой is in the instrumental case, because it comes after с in this expression.

The pattern is:

повезти кому? с чем?
= to get lucky with something

So:

• Мне повезло с квартирой.
• Нам повезло с работой.
• Ему повезло с соседями.

Here с does not literally mean physical company, like with a friend. It means something more like:

• when it came to
• in the matter of
• regarding

So с квартирой means with the apartment / as far as the apartment is concerned.

Usually it means you were lucky in connection with the apartment situation.

Depending on context, that could mean:

• you found a very good apartment
• the apartment was cheap
• the location was great
• the landlord was reasonable
• the timing worked out well
• the apartment turned out better than expected

So the phrase is fairly broad. It does not only mean I found an apartment. It means things went well for me regarding the apartment.

This is a question of aspect.

• повезло = perfective
  one completed lucky event, one successful outcome

• везло = imperfective
  ongoing, repeated, or general luck

So:

• Мне повезло с квартирой.
  = I got lucky with the apartment.
  (this specific case)

• Мне всегда везло с квартирами.
  = I’ve always been lucky with apartments.
  (general pattern / repeated experience)

In your sentence, Russian uses повезло because it is talking about one concrete result.

Yes. Russian word order is flexible, and changing it usually changes emphasis, not the core meaning.

For example:

• Мне повезло с квартирой.
  neutral, natural order

• С квартирой мне повезло.
  emphasizes the apartment: As for the apartment, I got lucky.

• Мне с квартирой повезло.
  also possible; a slightly different rhythm, but same basic meaning

So the original sentence is a very natural default version, but other orders are possible.

Yes. Just add не:

• Мне не повезло с квартирой.
  = I was unlucky with the apartment.

This can mean, for example, that the apartment was bad, too expensive, had problems, or the deal fell through.

The structure stays the same:

• мне = dative
• не повезло = was not lucky
• с квартирой = with the apartment

You usually use:

• Мне везёт с квартирами.
  = I’m lucky with apartments / I tend to be lucky with apartments.

• Мне повезёт с квартирой.
  = I’ll be lucky with the apartment.

Notice that the present meaning normally uses везёт rather than повезёт, because perfective verbs do not have a true present tense in Russian.

So:

• везёт = present / habitual
• повезло = past, one successful outcome
• повезёт = future, one expected successful outcome

Yes, very often. This is a productive and common pattern in Russian.

Examples:

• Мне повезло с работой.
  = I got lucky with the job.

• Нам повезло с погодой.
  = We got lucky with the weather.

• Ей повезло с мужем.
  = She got lucky with her husband.

• Им повезло с учителем.
  = They got lucky with the teacher.

So once you learn повезти кому-то с чем-то, you can use it in many situations.

Yes, it is the same preposition с, but here it is part of a set expression.

In English, with also does different jobs in different contexts, and Russian с works similarly. In this sentence, it does not mean simple accompaniment. Instead, it marks the thing in relation to which you were lucky.

So although the dictionary meaning is often with, in this sentence it is better understood as:

• with regard to
• in terms of
• when it came to

That is why translating word-for-word can feel strange, even though the Russian structure is perfectly normal.