Перед сном я проверяю, выключен ли телевизор.

Because перед in the meaning before normally takes the instrumental case.

• сон = sleep, a sleep
• Instrumental singular: сном

So:

• перед сном = before sleep, before going to bed

This is a very common Russian expression. A native English speaker can think of it as an idiomatic time phrase.

Literally, it means before sleep, but in natural English it usually means:

• before going to sleep
• before bed
• before I go to bed

It does not usually mean some abstract discussion of sleep in general. In everyday Russian, перед сном is a normal way to talk about something you do at night just before sleeping.

Проверяю is the imperfective present form of проверять.

Here it shows a habitual / repeated action:

• Перед сном я проверяю... = Before bed, I check...

That sounds like something the speaker does regularly.

Compare:

• я проверяю = I check / I am checking
• я проверю = I will check
• проверить = to check

So the sentence is talking about a routine, which is why проверяю is the natural choice.

Ли is a particle used to introduce an indirect yes/no question. In English, this is often translated as whether or sometimes if.

So:

• выключен ли телевизор = whether the TV is turned off

The whole sentence means something like:

• Before bed, I check whether the TV is off.

This is one of the most important uses of ли in Russian.

In Russian, ли usually comes after the word that is being focused on or after the first important element of the clause.

Here:

• выключен ли телевизор

The speaker is checking the state off or not off, so выключен comes first, and ли follows it.

This word order is very natural in Russian.

If you changed the order, the emphasis could change:

• Телевизор ли выключен... would sound like you are contrasting the TV with something else, which is not the neutral meaning here.

So выключен ли телевизор is the standard, neutral way to say whether the TV is off.

Выключен is the short form. Here it means a state:

• телевизор выключен = the TV is turned off

This is exactly what Russian normally uses after the implied verb to be in the present tense.

By contrast, выключенный is the full form, and it usually works more like an adjective before a noun:

• выключенный телевизор = a turned-off TV

So:

• Телевизор выключен = The TV is off.
• Выключенный телевизор стоял в углу = The turned-off TV stood in the corner.

In your sentence, the speaker is checking the TV’s condition, so выключен is correct.

Yes, in a way. Russian normally omits the present-tense form of быть in sentences like this.

So Russian says:

• телевизор выключен

where English says:

• the TV is off
• the TV is turned off

There is no separate present-tense is word in normal Russian sentences of this type.

So выключен ли телевизор literally works something like:

• turned off whether the TV [is]

but in natural English: whether the TV is turned off.

Because телевизор is the subject of the embedded clause:

• выключен ли телевизор = whether the TV is off

Even though the whole clause depends on проверяю, the noun телевизор is not the direct object of проверяю by itself.

The structure is:

• я проверяю
  • whole clause
• I check + whether the TV is off

Inside that clause, телевизор is the thing that is off / is not off, so it stays in the nominative.

Because выключен ли телевизор is a subordinate clause.

Russian uses a comma to separate the main clause from the subordinate clause:

• Я проверяю, выключен ли телевизор.

That comma is standard and required.

It is similar to English structure like:

• I check whether the TV is off.

English often does not need a comma there, but Russian does.

Usually, in a neutral sentence, many speakers would write this without that comma:

• Перед сном я проверяю, выключен ли телевизор.

The comma after Перед сном can reflect a pause or intonation, but it is often omitted in straightforward neutral writing.

So for learners, the safest neutral version is:

• Перед сном я проверяю, выключен ли телевизор.

The really important comma is the one before the ли-clause.

Because Russian has no articles.

So Russian does not have separate words corresponding to English a and the.

• телевизор can mean a TV or the TV
• context tells you which one is meant

In this sentence, the context makes it clear that we mean the TV.

Yes. In natural English, both are possible:

• I check whether the TV is off.
• I check if the TV is off.

But grammatically, Russian ли corresponds most directly to whether in an indirect yes/no question.

So if you want the clearest grammar match:

• ли = whether

But in everyday English translation, if is often perfectly natural.