hokensyou wo motanai mama ie wo dete simatte, eki de kidukimasita.

In this sentence, 〜まま means while still in that state or without changing that condition.

So:

• 保険証を持たないまま = without having my insurance card on me
• more literally: remaining in the state of not carrying my insurance card

It often describes doing something while a previous situation stays unchanged.

A useful pattern is:

• Verbない-form + まま = without doing ...
• Noun + の + まま = as it is / still ...

Examples:

• 朝ごはんを食べないまま学校へ行った。
  = I went to school without eating breakfast.
• 靴のまま入らないでください。
  = Please don’t come in with your shoes on.

Both can be possible, but 持たないまま is very natural here.

• 持たないまま focuses on not taking/carrying it
• 持っていないまま focuses on being in the state of not having it

In everyday situations like forgetting to bring something, Japanese often uses the simpler ない-form + まま:

• 財布を持たないまま出かけた。
  = I went out without bringing my wallet.

So 保険証を持たないまま家を出てしまって means something like:

• I left home without bringing my insurance card
• I went out still not carrying my insurance card

〜てしまう often adds one of these meanings:

1. completion: doing something completely
2. regret / accidental action / “oops” feeling

Here it mainly gives the second nuance.

• 家を出てしまって = I ended up leaving the house / I left the house and unfortunately...

It suggests the speaker realizes this was not ideal. It sounds like:

• I went and left home without my insurance card...
• I accidentally left home without it...

Without しまう, the sentence would still be grammatical:

• 保険証を持たないまま家を出て、駅で気づきました。

But しまって adds the feeling of oops / unfortunately.

The て at the end connects this part to the next clause.

The sentence is:

• 保険証を持たないまま家を出てしまって、駅で気づきました。

This means:

• I left home without my insurance card, and then I noticed at the station.

So 〜て links events in sequence.

A very literal breakdown is:

• 保険証を持たないまま = without bringing my insurance card
• 家を出てしまって = I ended up leaving home
• 駅で気づきました = I noticed at the station

So the flow is:

1. did not have the insurance card
2. left home anyway
3. noticed it at the station

Both exist, but 家を出る is the normal expression for leave the house/home.

With verbs of movement, を can mark the place one passes through or leaves:

• 家を出る = leave the house
• 電車を降りる = get off the train
• 道を歩く = walk along the road

家から出る is also possible, but it feels more like emphasizing the starting point: go out from the house.

In most ordinary situations, 家を出る is the most natural way to say leave home.

Because 保険証 is the direct object of 持たない.

• 保険証を持たない = not carry / not have the insurance card with you

So there are two different を particles in the sentence, but they belong to different verbs:

1. 保険証を持たない
   
   • 保険証 is the object of 持つ
2. 家を出る
   
   • 家 is the place being left

This is completely normal in Japanese.

気づく means to notice, to realize, or to become aware of something.

Here, the thing being noticed is understood from context:

• (保険証を持っていないことに) 気づきました
• I realized (that I didn’t have my insurance card).

Japanese often leaves out information that is obvious from context, so the sentence does not need to explicitly say what was noticed.

If you wanted to say it fully, you might say:

• 駅で保険証を持っていないことに気づきました。
  = I realized at the station that I didn’t have my insurance card.

Because 駅で marks the place where the noticing happened.

• 駅で気づきました = I noticed it at the station

Here, で is the location of the action/event.

By contrast, に気づく is used for the thing you notice:

• 間違いに気づく = notice a mistake
• 音に気づく = notice a sound
• 忘れ物に気づく = notice something was forgotten

So in a fuller version, you could have both:

• 駅で、保険証を忘れたことに気づきました。
  = At the station, I realized I had forgotten my insurance card.

Here:

• 駅で = where I realized it
• 〜ことに = what I realized

Yes, in everyday Japanese 保険証 usually refers to a health insurance card.

It is short for something like 健康保険証.

Depending on context, it may be translated as:

• insurance card
• health insurance card

If the meaning has already been given to the learner, the main thing to know is that Japanese speakers commonly just say 保険証 in daily life.

It breaks down like this:

• 保険証を持たないまま
  = without bringing my insurance card / still not having my insurance card on me

• 家を出てしまって、
  = I ended up leaving home, and...

• 駅で気づきました。
  = I noticed at the station.

So the whole sentence means something like:

• I left home without my insurance card and noticed it at the station.
• with a bit more nuance: I ended up leaving home without my insurance card, and then realized it at the station.

The sentence naturally tells the events in order.

Yes. Japanese often omits the subject when it is clear from context.

This sentence does not explicitly say I, but that is the natural interpretation:

• (私は) 保険証を持たないまま家を出てしまって、駅で気づきました。

So the speaker is understood to be the person who:

1. did not bring the insurance card
2. left home
3. noticed it at the station

In English, you usually need I, but in Japanese it is often unnecessary.

Yes. In normal Japanese writing, punctuation can vary a little.

You might see:

• 保険証を持たないまま家を出てしまって、駅で気づきました。
• 保険証を持たないまま家を出てしまって駅で気づきました。

The comma just makes the sentence easier to read by showing the pause before the final result.

Also, Japanese is normally written without spaces, so a natural written version is:

• 保険証を持たないまま家を出てしまって、駅で気づきました。

The spaces in learner materials are just there to help with reading.