Muszę wyłączyć lampę przed snem.

Because Polish usually drops subject pronouns when they are not needed.

Muszę already tells you the subject is I, because the verb ending -ę marks 1st person singular.

So:

• Muszę = I must / I have to
• Ja muszę = I must, but with extra emphasis on I

You would add ja only if you want contrast or emphasis, for example:

• Ja muszę wyłączyć lampę, a ty nie.
  I have to turn off the lamp, but you do not.

Muszę is the 1st person singular present tense form of the verb musieć.

Conjugation:

• muszę = I must
• musisz = you must
• musi = he/she/it must
• musimy = we must
• musicie = you all must
• muszą = they must

So in this sentence, muszę means I have to or I must.

Because after musieć, Polish normally uses an infinitive.

So the structure is:

• muszę + infinitive
• I have to + verb

Examples:

• Muszę iść. = I have to go.
• Muszę pracować. = I have to work.
• Muszę wyłączyć lampę. = I have to turn off the lamp.

This is very similar to English have to + verb.

This is about aspect, which is very important in Polish.

• wyłączyć = perfective
• wyłączać = imperfective

Here, wyłączyć focuses on completing the action: turning the lamp off successfully.

So:

• Muszę wyłączyć lampę = I need to turn the lamp off
• Muszę wyłączać lampę = I have to turn the lamp off regularly / as a repeated habit / keep doing that kind of action

In this sentence, the perfective form sounds natural because the speaker means one complete action that should happen before sleep.

Because lampę is the accusative singular form of lampa.

The verb wyłączyć takes a direct object, and direct objects often go in the accusative case.

So:

• lampa = nominative, dictionary form
• lampę = accusative singular

This is a very common pattern for feminine nouns ending in -a:

• książka → książkę
• kawa → kawę
• lampa → lampę

Yes, and it would slightly change the focus.

• wyłączyć lampę = turn off the lamp
• wyłączyć światło = turn off the light

In everyday speech, both can make sense, depending on what exactly you mean:

• lampę focuses more on the device
• światło focuses more on the illumination

If you mean a bedside lamp, lampę is perfectly natural.

Przed requires the instrumental case, so sen changes to snem.

So:

• sen = sleep, dream
• przed snem = before sleep / before going to sleep

This is a fixed and very common expression.

More examples with przed + instrumental:

• przed obiadem = before lunch
• przed pracą = before work
• przed szkołą = in front of the school / before school, depending on context

In your sentence, przed snem is a time expression meaning before going to sleep.

Yes, sen can mean both sleep and dream, depending on context.

In przed snem, it clearly means before sleep or before going to bed.

So although the noun has more than one possible meaning, the phrase przed snem is understood naturally as a time expression related to sleeping, not dreaming.

Yes. That is another natural way to say it.

Compare:

• przed snem = before sleep / before bed
• przed pójściem spać = before going to sleep

The second version is a bit more explicit and a little longer.
The original przed snem is shorter and very idiomatic.

Polish word order is fairly flexible.

The original sentence:

• Muszę wyłączyć lampę przed snem.

is neutral and natural.

You can also say:

• Przed snem muszę wyłączyć lampę.

This puts more emphasis on before sleep.

In English, word order is much stricter. In Polish, changing the order often changes emphasis rather than the basic meaning.

A few parts may be tricky:

• muszę
  The sz sounds like English sh.
  The final ę is a nasal vowel; in normal speech it is often less strongly nasal than learners expect.

• wyłączyć
  ł sounds like English w.
  cz sounds like ch in chop.
  So wyłączyć sounds roughly like vih-WON-chich or vih-WON-chyć, depending on how detailed you want to be with the final sound.

• przed
  The rz here sounds like zh, somewhat like the sound in measure.

• snem
  The sn cluster is pronounced directly, with no extra vowel inserted.

A learner-friendly rough guide for the whole sentence is:

MOO-sheh vih-WON-chich LAM-peh pshet snem

That is only approximate, but it can help at first.

Usually it can mean either, depending on context.

• I must turn off the lamp before sleep
• I have to turn off the lamp before sleep

In everyday English, I have to often sounds more natural.
In Polish, muszę covers both ideas very well.

If the speaker wants to sound softer, other structures are also possible, but muszę is the straightforward, standard choice.