hokensyou ga kaban no naka ni atte, hottosimasita.

が marks 保険証 as the thing whose existence is being stated: the insurance card was in the bag.

With ある, Japanese often uses が for the thing that exists and に for the place:

• 保険証がある = there is an insurance card / the insurance card is there
• かばんの中にある = it is in the bag

If you used は instead, the nuance would shift more toward as for the insurance card..., which is possible in some contexts, but が is the most natural choice here when simply stating that it was there.

かばんの中に means in the bag.

It breaks down like this:

• かばん = bag
• の = links nouns, like of or an apostrophe-s
• 中 = inside
• に = marks the location where something exists

So:

• かばんの中 = the inside of the bag
• かばんの中にある = to be in the bag

に is used because ある expresses existence in a place.
Compare:

• 机の上に本がある = There is a book on the desk.
• 公園で遊ぶ = Play in the park.

With ある/いる, the location is usually marked by に, not で.

の connects nouns. Here it links かばん and 中.

• 中 is a noun meaning inside or middle
• かばんの中 literally means the bag's inside or the inside of the bag

This pattern is very common:

• 箱の中 = inside the box
• 部屋の中 = inside the room
• ポケットの中 = inside the pocket

So の is just the normal way to attach one noun to another in Japanese.

Yes. あって is the て-form of ある.

• dictionary form: ある
• て-form: あって
• past polite: ありました

In this sentence, the て-form connects two ideas:

1. 保険証がかばんの中にあって = the insurance card was in the bag / I found that it was in the bag
2. ほっとしました = I felt relieved

So the sentence structure is basically:

[It was in the bag], and [I felt relieved].

The て-form often links events or states and can also imply a reason or background, which it does here.

Literally, it means was there.
But in context, it often strongly suggests it turned out to be there or I found it there.

So the Japanese does not directly say I found the insurance card, but the natural implication is something like:

• it was in the bag
• and because of that, I felt relieved

If the speaker wanted to say I found it more explicitly, they might say:

• 保険証が見つかって、ほっとしました。
  = I found the insurance card / The insurance card was found, and I felt relieved.

Your sentence focuses more on the fact that it was in the bag.

Because Japanese often leaves out subjects when they are clear from context.

In ほっとしました, the subject is not stated, but it is naturally understood as I in many situations:

• (私は) ほっとしました = I felt relieved

Japanese frequently omits words like I, you, or it if the listener can figure them out. That is very normal and natural.

So even though the sentence does not explicitly say I, the meaning is understood from context.

ほっとしました means something like:

• I felt relieved
• I was relieved
• What a relief

It often has the nuance of tension or worry suddenly easing.

安心しました also means I felt relieved or I felt reassured, but it can sound a little more neutral or formal.
ほっとしました feels more like the emotional release after concern.

For example:

• 間に合って、ほっとしました。
  = I made it in time, and I felt relieved.

• 安全だと分かって、安心しました。
  = I learned it was safe, and I felt reassured.

In your sentence, ほっとしました fits very naturally because the speaker was probably worried about the missing insurance card.

Because the feeling of relief happened at that moment in the past.

The sentence is describing a completed reaction:

• the speaker realized the insurance card was in the bag
• then the speaker felt relieved

So ほっとしました is past because it reports what happened.

Even if the insurance card is still in the bag now, the relief itself is treated as a past event.

Yes.

In normal Japanese writing, spaces are usually not used, so it would normally appear as:

保険証がかばんの中にあって、ほっとしました。

The comma 、 is also common here because it helps separate the two parts of the sentence, but in some casual writing it might be omitted:

保険証がかばんの中にあってほっとしました。

That said, the version with the comma is easier to read.

The sentence uses the polite ます style:

• しました = polite past
• plain form would be した

So the plain-style version would be:

保険証がかばんの中にあって、ほっとした。

Both are grammatically correct. The difference is tone:

• ほっとしました = polite, neutral, appropriate in many everyday situations
• ほっとした = casual, plain

Textbook example sentences often use the polite style unless there is a reason to be casual.

Yes, it is possible, but the nuance changes.

• 保険証が... focuses on the existence/discovery of the insurance card
• 保険証は... treats the insurance card as the topic, something already under discussion

So:

• 保険証がかばんの中にあって、ほっとしました。
  sounds like The insurance card was in the bag, and I was relieved.

• 保険証はかばんの中にあって、ほっとしました。
  sounds more like As for the insurance card, it was in the bag, and I was relieved.

In this situation, が is usually the more natural default choice.