Megnézem, bezártam-e a garázst, mielőtt lefekszem.

Hungarian often uses the present tense to talk about a future action, especially when the future is clear from context.

So Megnézem literally looks like I check / I am checking, but here it means I’ll check.

This is very normal in Hungarian:

• Holnap megyek. = I’m going tomorrow.
• Mindjárt megnézem. = I’ll check right away.

In your sentence, the context makes the future meaning clear:

• Megnézem ... mielőtt lefekszem.
  = I’ll check ... before I go to bed.

meg- is a verbal prefix. In many verbs, it adds a sense of completion, result, or doing something properly / to the end.

Compare:

• nézem = I look at / watch
• megnézem = I check / I take a look / I look and find out

So here megnézem is not just I look, but more like I check or I make sure.

The -e particle marks an indirect yes/no question. Here it means something like whether or if.

So:

• bezártam-e a garázst = whether I locked the garage

This is a very common Hungarian structure:

• Nem tudom, otthon van-e. = I don’t know whether he/she is at home.
• Megkérdezem, jön-e. = I’ll ask whether he/she is coming.

A very important point: -e is attached to the finite verb, usually with a hyphen:

• bezártam-e
• jön-e
• van-e

Because the speaker is checking whether the garage was already locked earlier.

• bezártam = I locked it / I have locked it
• bezárom = I lock it / I will lock it

The idea is:

• first, maybe at some earlier moment, I locked the garage
• now, before bed, I check whether I did that

So Hungarian uses the past tense because the locking is viewed as a completed earlier action. In English, this often corresponds to the present perfect:

• bezártam-e a garázst = whether I locked / have locked the garage

For the same reason as megnézem: Hungarian often uses the present tense for future events when the time reference is clear.

• mielőtt lefekszem = before I go to bed

English does something similar here:

• not usually before I will go to bed
• but before I go to bed

So this part is actually quite close to English usage.

lefekszem comes from lefeküdni / lefeküdik, which literally has the idea of lying down.

In everyday Hungarian, it commonly means:

• to go to bed

So:

• mielőtt lefekszem = before I go to bed

The prefix le- often has a sense of downward movement, so the literal background is something like lie down.

The -t marks the accusative case, which is used for the direct object.

Here, the thing being locked is the garage, so it takes -t:

• a garázs = the garage
• a garázst = the garage as a direct object

This is very common in Hungarian:

• látom a házat = I see the house
• bezárom az ajtót = I lock the door

So:

• bezártam a garázst = I locked the garage

Because Hungarian has two forms of the definite article:

• a before a consonant
• az before a vowel

Since garázs begins with g, you use a:

• a garázs
• a garázst

Compare:

• az ajtó = the door
• az autó = the car

Because the verb is in the definite conjugation.

Hungarian verbs have two main conjugation patterns:

• indefinite
• definite

You usually use the definite conjugation when the verb has a definite object. Here, the object is the whole clause:

• bezártam-e a garázst

That clause functions as what is being checked, so megnézem is natural.

Compare:

• Nézek valamit. = I’m looking at something.
• Nézem a filmet. = I’m watching the film.

Similarly:

• Megnézem. = I’ll check it / I’ll check whether...

Yes. It is an embedded clause functioning as the object of megnézem.

Very roughly, the structure is:

• Megnézem
  = I’ll check
• bezártam-e a garázst
  = whether I locked the garage
• mielőtt lefekszem
  = before I go to bed

So the whole sentence is:

[I’ll check] [whether I locked the garage] [before I go to bed].

Because Hungarian normally separates subordinate clauses with commas.

Here:

• Megnézem, bezártam-e a garázst, mielőtt lefekszem.

The clause bezártam-e a garázst is inserted after the main verb, and mielőtt lefekszem is another subordinate clause, so commas are used to mark the clause boundaries.

This is more systematic in Hungarian than in English.

Yes. Hungarian word order is fairly flexible, although different orders may change the focus or what sounds most natural.

For example, you could also say:

• Mielőtt lefekszem, megnézem, bezártam-e a garázst.

This puts before I go to bed first.

The original sentence is very natural because it presents the main action first:

• Megnézem = I’ll check
• then what is being checked
• then the time frame

In this sentence, -e is enough, and it is the most important marker.

So:

• bezártam-e a garázst = whether I locked the garage

Hungarian often uses -e where English uses if/whether in indirect questions.

A learner should especially remember this pattern:

• finite verb + -e

For example:

• tudom-e
• jön-e
• bezártam-e

You can break it down like this:

• be- = a verbal prefix, here giving the sense of closed/shut
• zár = the verb stem close / lock
• -t- = past tense marker
• -am = I ending (1st person singular)

So bezártam means:

• I locked
• or, depending on context, I have locked

This kind of breakdown can be very helpful when learning Hungarian verb forms.