kasa wo wasuretakoto ni kiduite, ie made hikikaesu ka douka sukosi mayoimasita.

Because 気づく usually takes a noun-like thing as what you notice.

• 忘れた by itself is just a verb phrase: forgot
• 忘れたこと turns that whole idea into a noun-like expression: the fact that I forgot it

So:

• 傘を忘れたことに気づく = to realize that I forgot my umbrella

This こと is very common when Japanese wants to treat an action or event as a thing.

Often, yes.

• 傘を忘れたことに気づく
• 傘を忘れたのに気づく

Both can mean to realize that I forgot my umbrella.

A useful rough guideline:

• の can sound a bit more direct or immediate
• こと can sound a bit more neutral or matter-of-fact

In many everyday sentences, the difference is small, and both are natural.

気づく means to notice or to realize.

The particle に marks the thing that you become aware of.

So:

• 忘れたことに気づく = to realize the fact that you forgot it

The -て form, 気づいて, connects this to the next action:

• I realized I had forgotten my umbrella, and then...

So the sentence flows as:

1. realized the umbrella was forgotten
2. then felt unsure about turning back home

The -て form links actions or events.

Here it means something like:

• after realizing...
• realizing that..., I...

So:

• 傘を忘れたことに気づいて、家まで引き返すかどうか少し迷いました。

has the sense of:

• After realizing I had forgotten my umbrella, I hesitated a little about whether to turn back home.

It shows that the realization happened first, and the hesitation came after.

Here, まで means as far as or to.

So:

• 家まで引き返す = turn back as far as home / go back home

まで can mean until in time expressions, but with places it often marks a destination or endpoint.

Examples:

• 駅まで行く = go to the station
• 家まで戻る = go back home

So in this sentence, 家まで is about location, not time.

引き返す means to turn back, to go back the way you came, or to retrace your steps.

It is a little more specific than just 戻る.

• 戻る = return/go back
• 引き返す = turn around and head back from where you are

So this sentence suggests the speaker was already on the way somewhere, then realized the umbrella was missing, and considered reversing course to go home.

Because the speaker is wondering about a possible action, not checking whether the action already happened.

かどうか often follows the plain form when it means whether or not to do X or whether X will happen.

Here:

• 引き返すかどうか迷いました = I hesitated about whether to turn back

If you said 引き返したかどうか, that would mean:

• whether I turned back or not

That would sound like you are uncertain about a completed past event, which is not the meaning here.

かどうか means whether or not.

So:

• 家まで引き返すかどうか = whether or not to turn back home

This whole part becomes the content of what the speaker was unsure about.

You can think of it like:

• I was unsure: Should I turn back home, or not?

That is why 迷いました follows it naturally.

No. Here 迷う does not mean physically getting lost.

In this context, 迷う means:

• to hesitate
• to be unsure
• to waver between options

So:

• 少し迷いました = I hesitated a little / I was a little unsure

It suggests the speaker thought briefly about the decision, rather than being completely unable to decide.

Japanese often leaves the subject unstated when it is clear from context.

In this sentence, the same person is understood to be:

• the one who forgot the umbrella
• the one who realized it
• the one who considered turning back
• the one who hesitated

So English needs I, but Japanese does not.

This is very normal in Japanese. The subject is often omitted when it would be obvious to the listener or reader.

With 忘れる, the thing forgotten is marked by を.

So:

• 傘を忘れる = to forget an umbrella
• 財布を忘れる = to forget a wallet

This is a very standard verb-particle combination in Japanese.

In this sentence:

• 傘を忘れたこと = the fact that I forgot my umbrella

So the を belongs to 忘れた, not to こと.

It is helpful, but not grammatically essential.

The comma shows a pause and makes the structure easier to read:

• realizing I had forgotten my umbrella, ...

Japanese punctuation is often used more flexibly than English punctuation. The sentence would still be understandable without the comma, but the comma makes the transition between the two parts clearer.