Learn Hardcore Japanese: genkan no kagami wo mite kara, gakkou ni dekakemasu. - I look in the mirror at the entrance and then leave for school.

It’s not just the door itself. In English you might translate it as entrance, entryway, or foyer, depending on the house.
So 玄関の鏡 means the mirror in/by the entrance area of the house.

Why is の used between 玄関 and 鏡?

の links two nouns and often shows:

possession: 私の本 = my book
belonging/location: 学校の先生 = teacher of the school
characteristic: 日本の会社 = Japanese company

Here, 玄関の鏡 literally is the mirror of the entrance, meaning the mirror that is in the entrance area / entrance mirror.

So 玄関の鏡 is a fixed noun phrase: a specific mirror associated with the entrance.

Why does 鏡 take the particle を?

を marks the direct object of a transitive verb.

The verb here is 見る (to look at, to see).
The thing you look at is 鏡 (the mirror).

So:

鏡を見ます = (I) look at the mirror.

In the sentence:

玄関の鏡を見てから
→ after (I) look at the entrance mirror …

In casual speech, を can sometimes be dropped in conversation, but in correct standard Japanese it’s used here.

What is the role of て in 見て?

見て is the て-form of 見る.

The て-form is used for many things; here it’s used in the pattern:

verb て + から

This pattern means “after doing X, (do Y)”.

So 見てから = after looking (at it).
The て itself is a connector that lets you attach から and show a sequence of actions.

What does 〜てから mean, and how is it different from using から by itself or using 前に?

〜てから means:

after doing X, (do Y)

Pattern: Vてから、 main action

In this sentence:

玄関の鏡を見てから、学校に出かけます。
→ After looking at the entrance mirror, (I) leave for school.

Differences:

〜てから vs から with plain form
- 雨が降ったから、行きません。
  Because it rained, I won’t go.
- 雨が降ってから、行きました。
  After it rained, I went.
With てから, the main meaning is time/sequence (“after”), not “because”.
〜てから vs 〜前に
- 出かける前に、玄関の鏡を見ます。
  Before going out, I look at the entrance mirror.
- 玄関の鏡を見てから、出かけます。
  After looking at the entrance mirror, I go out.

They describe the order from different reference points:

前に: “before doing Y, do X”
てから: “after doing X, do Y”

Both can describe similar routines but from opposite sides of the timeline.

Why is に used after 学校? Could we use へ instead?

Here, 学校に marks the destination (“to school”).

場所 + に is used with verbs of movement to show where you go to:
学校に行きます = (I) go to school.

You could say 学校へ出かけます, and it is grammatically correct:

に often emphasizes the target/destination.
へ emphasizes the direction (toward).

In everyday speech, 学校に出かけます is natural and common. へ sounds a bit more formal or literary.

What’s the difference between 出かけます and 行きます, and why 出かけます here?

Both 出かけます and 行きます involve going somewhere, but their focus is different:

行きます = to go (to some place)
Focus: moving from here to there.
出かけます = to go out / to leave home (or where you are)
Focus: leaving your current place, usually for some purpose (work, school, shopping, etc.)

In this sentence:

学校に出かけます
→ (I) go out (leave home) to go to school.

It highlights the act of going out from home for school, not just the simple movement “go to school.” You could say 学校に行きます, but 出かけます matches the idea of a morning routine of “going out of the house.”

What tense is 出かけます here? Does it mean present, future, or habitual?

出かけます is the polite non-past form.

Non-past in Japanese covers:

present habitual: I (usually) go out…
general truth: I go out (as a rule)…
near future: I will go out / I’m going out (soon)…

In a sentence like this, describing a routine:

玄関の鏡を見てから、学校に出かけます。
→ It naturally reads as a habitual action:
“I (usually) look at the mirror in the entrance and then go to school.”

Where is the word “I” in this sentence? How would you say I explicitly?

Japanese often omits the subject when it’s clear from context. Here, the subject is understood as “I” (or “we,” or “he/she,” depending on context).

If you want to say “I” explicitly, you can add it at the beginning:

私は玄関の鏡を見てから、学校に出かけます。
→ As for me, after looking at the entrance mirror, I go to school.

Other possible subjects (depending on context) could be 彼は (he), 妹は (my younger sister), etc.

Could we say 玄関で鏡を見てから instead of 玄関の鏡を見てから? What’s the difference?

Yes, and the nuance is slightly different.

玄関の鏡を見てから…
- Focuses on a specific mirror associated with the entrance.
- “After looking at the entrance mirror …”
玄関で鏡を見てから…
- で marks the location where the action happens.
- “After looking in a mirror in the entrance area …”
- It doesn’t emphasize that the mirror is “the entrance mirror” as a named item; just that the action takes place there.

In many real situations, both could describe the same scene, but 玄関の鏡 sounds like the mirror that is (almost permanently) there, while 玄関で鏡 describes where you look in a mirror.

Is the word order fixed, or can I move parts of the sentence around?

Japanese word order is flexible, but there are natural patterns.

The basic pattern here is:

(time/condition clause) + main clause
玄関の鏡を見てから、学校に出かけます。

This is natural: “After doing X, I do Y.”

You can sometimes shuffle phrases like 学校に, but you cannot break up the grammar unit 見てから or separate 学校に from 出かけます in a weird way.

For example:

学校に、玄関の鏡を見てから出かけます。
→ possible, but feels a bit clunky; the original is smoother.
✗ 学校に出かけます玄関の鏡を見てから。
→ unnatural; the “after” clause (見てから) should come before the main action.

A safe rule: keep [verb て + から] together, and put that clause before the main action.

What is the difference between 出かけます and 出かける here?

They are the same verb 出かける (“to go out”), in different forms:

出かける = plain (dictionary) form, non-past
出かけます = polite ます form, non-past

Use:

出かけます when speaking politely (to teachers, strangers, in most textbooks).
出かける when speaking casually with friends or in informal writing.

So in casual speech, the sentence could be:

玄関の鏡を見てから、学校に出かける。