Свет уже включён в коридоре.

In Russian, the verb to be is normally omitted in the present tense.

So:

• Свет включён = The light is on / The light is switched on
• literally, Russian just says something like Light switched-on

This is completely normal. You do not need a present-tense есть here.

Уже means already.

So:

• Свет включён = The light is on
• Свет уже включён = The light is already on

It adds the idea that this happened earlier than expected, or that the result is already true.

Включён is the short passive participle of включить (to switch on / to turn on).

In this sentence, it describes the resulting state:

• Свет включён = The light is switched on / is on

This is very common in Russian for talking about states that result from an action.

Compare:

• Я включил свет = I turned on the light
  (action)
• Свет включён = The light is on / has been turned on
  (resulting state)

Because свет is a masculine singular noun, and the short participle has to agree with it.

Agreement here is:

• masculine singular: включён
• feminine singular: включена
• neuter singular: включено
• plural: включены

Examples:

• Лампа включена. = The lamp is on.
• Окно открыто. = The window is open.
• Фары включены. = The headlights are on.

Because свет is the grammatical subject of the sentence.

The sentence is about the light and its state:

• Свет = subject
• включён = what is said about the subject

So nominative is expected.

Because this sentence describes location, not motion.

• в коридоре = in the hallway / corridor
  (where something is)
• в коридор = into the hallway / corridor
  (movement toward)

Here the light is already on in that place, so Russian uses в + prepositional:

• в коридоре

Коридоре is the prepositional case singular form of коридор.

The preposition в can take different cases depending on meaning:

• в коридоре = in the corridor → location → prepositional
• в коридор = into the corridor → direction/motion → accusative

So:

• dictionary form: коридор
• in this sentence: в коридоре

Usually свет here means the light / the lighting in a room or area, not necessarily one specific lamp.

So Свет уже включён в коридоре most naturally means:

• The light is already on in the hallway

Russian often uses свет this way when talking about whether lighting is on or off.

Yes. Russian word order is flexible, and changing it often changes emphasis rather than basic meaning.

Possible versions:

• Свет уже включён в коридоре.
  neutral
• В коридоре свет уже включён.
  emphasizes in the hallway
• Уже включён свет в коридоре.
  more marked, often literary or contextual

A learner should treat Свет уже включён в коридоре as a normal, neutral sentence.

Often, yes.

In many contexts, Russian uses включён / выключен where English prefers on / off:

• Телевизор включён. = The TV is on.
• Свет включён. = The light is on.

So although включён literally comes from switch on, the best English translation is often just on.

The correct spelling is включён, with ё, and the stress falls there:

• в-клю-чён

In many Russian texts, ё is often written as е, so you may also see включен. But the pronunciation is still включён.

That matters because ё clearly shows both:

• the correct stress
• the yo sound

A helpful pronunciation guide is:

Svyet u-ZHÉ v-klyu-CHYON f ka-ri-DO-re

A few key points:

• Свет sounds roughly like svyet
• уже is stressed on the second syllable: уже́
• включён is stressed on the last syllable: включён
• в коридоре has stress on -до-: коридо́ре

Also note that в before коридоре is pronounced more like f because of sound assimilation:

• в коридоре → roughly f kariDOre

Grammatically, yes, but it is less neutral in everyday speech.

• включён is the normal word for electric lights being turned on
• зажжён literally means lit / ignited and feels more natural with fire, candles, or in a more literary style

So for ordinary hallway lighting, включён is the most natural choice.

It mainly focuses on the state/result.

• Свет уже включён = the light is already in the on state

If you wanted to focus on the action itself, you would use a finite verb, for example:

• Свет уже включили в коридоре. = They already turned on the light in the hallway.

So the original sentence is more about the current situation than about who did it.