Выключенный телевизор стоит в углу, и в комнате тихо.

Because выключенный is the full passive participle being used like an adjective before the noun телевизор.

• выключенный телевизор = the switched-off TV
• Телевизор выключен = The TV is switched off

So in your sentence, выключенный is part of the noun phrase and describes which TV we mean.

It is a past passive participle from the verb выключить.

That means it describes something that has had an action done to it:

• выключить = to switch off
• выключенный = switched off

In this sentence, it works just like an adjective and agrees with телевизор in:

• gender: masculine
• number: singular
• case: nominative

That is why it has the form выключенный.

Because it is the subject of the verb стоит.

The basic structure is:

• Выключенный телевизор стоит в углу.
• The switched-off TV is standing/is in the corner.

The thing doing the standing / being located is the TV, so телевизор is in the nominative.

Russian often uses position verbs like:

• стоять = stand
• лежать = lie
• сидеть = sit

for the physical position of objects.

So телевизор стоит в углу is very natural Russian. It means the TV is positioned there, not that it is actively standing like a person.

You could translate it naturally into English as:

• The switched-off TV is in the corner

But in Russian, стоит sounds normal and idiomatic.

Both are in the prepositional case because в is being used to mean in for a location.

Here the question is where?

• в углу = in the corner
• в комнате = in the room

So:

• угол → в углу
• комната → в комнате

This is the normal pattern for location with в.

Because угол has an irregular prepositional singular form: в углу.

This is just something you learn as a fixed form:

• угол = corner
• в углу = in the corner

Russian has a small group of nouns with special location forms like this.

Because in the present tense, Russian usually does not use a word for is/are.

So:

• в комнате тихо literally looks like
• in the room quiet

but it means:

• it is quiet in the room

This is completely normal Russian. The idea of is is understood.

Because тихо is not describing a noun here. It describes the general state of the room/environment.

Compare:

• тихая комната = a quiet room
  
  • Here тихая is an adjective modifying комната.
• В комнате тихо = It is quiet in the room
  
  • Here тихо is a predicative word/adverb-like form describing the situation.

So тихо is the correct form when you mean it is quiet.

Yes. It separates two coordinated clauses:

1. Выключенный телевизор стоит в углу
2. в комнате тихо

Even though the second clause has no visible is, it still functions as a full clause in Russian, so the comma is standard.

Yes. Russian word order is flexible.

For example:

• Выключенный телевизор стоит в углу, и в комнате тихо.
• В углу стоит выключенный телевизор, и в комнате тихо.

Both are correct.

The difference is mostly one of emphasis:

• starting with Выключенный телевизор highlights the TV first
• starting with В углу highlights the location first

Russian often changes word order to control focus and style more than basic grammar.

They are similar in meaning, but the structure is different.

• Выключенный телевизор стоит в углу
  = The switched-off TV is standing in the corner
  Here выключенный is part of the noun phrase.

• Телевизор выключен и стоит в углу
  = The TV is switched off and is standing in the corner
  Here выключен is a predicate, a separate statement about the TV.

The first version is more compact and descriptive. The second sounds more like two facts being stated.

It comes from выключить, the perfective verb.

• выключать = to be switching off / to switch off habitually
• выключить = to switch off completely

The participle выключенный expresses a completed result: the TV has already been switched off.

That is why perfective выключить is the source here.