Vous êtes autorisés à entrer dans cette pièce, et on vous autorise aussi à utiliser votre téléphone.

Because être autorisé à + infinitive means to be allowed/authorized to do something, while pouvoir usually means can / be able to.

So:

• Vous êtes autorisés à entrer = You are allowed to enter
• Vous pouvez entrer = You can enter

In many situations, vous pouvez entrer is perfectly natural and may even sound more common in everyday speech. But vous êtes autorisés à entrer stresses permission, not just ability.

So the sentence is specifically about what is permitted.

Because autorisés is an adjective/past participle used with être, and it agrees with vous.

Here, vous refers to more than one person, so the masculine plural form is used:

• masculine singular: autorisé
• feminine singular: autorisée
• masculine plural: autorisés
• feminine plural: autorisées

Examples:

• to one man: Vous êtes autorisé à entrer.
• to one woman: Vous êtes autorisée à entrer.
• to several people, at least one male or mixed group: Vous êtes autorisés à entrer.
• to several women: Vous êtes autorisées à entrer.

If vous is singular and formal, the form still agrees with the actual person being addressed.

Because autoriser follows the pattern:

• autoriser quelqu’un à faire quelque chose
• to allow someone to do something

So:

• autoriser quelqu’un à entrer
• autoriser quelqu’un à utiliser son téléphone

And in the passive-style structure:

• être autorisé à faire quelque chose

Examples:

• Je suis autorisé à partir. = I am allowed to leave.
• Elle est autorisée à conduire. = She is allowed to drive.

So the à is required by the verb pattern.

They express almost the same basic idea, but the structure is different:

• vous êtes autorisés à entrer = you are allowed to enter
• on vous autorise à utiliser votre téléphone = you are being allowed / people allow you to use your phone

The first is a passive-type structure with être.
The second is an active structure with on as the subject.

So the sentence combines:

1. a passive-style wording: you are authorized
2. an active wording: someone/people/we authorize you

French often mixes structures like this naturally.

A more parallel version could be:

• Vous êtes autorisés à entrer dans cette pièce et à utiliser votre téléphone.

Or:

• On vous autorise à entrer dans cette pièce et à utiliser votre téléphone.

In this sentence, on means something like people, they, someone, or we, depending on context.

So:

• on vous autorise literally = one authorizes you
• natural English = you are authorized / allowed

Here, on does not refer to one specific person. It is an indefinite subject.

Very often in French, on is used where English prefers a passive:

• On vous demande de patienter. = You are asked to wait.
• On vous autorise à entrer. = You are allowed to enter.

So in this sentence, on means the relevant authority / the people in charge / whoever is giving permission.

Because the two vous have different grammatical roles:

• Vous êtes autorisés...
  Here vous is the subject = you
• on vous autorise...
  Here vous is the object = authorizes you

So the sentence means:

• You are allowed to enter...
• ...and someone also allows you to use your phone.

This repetition is completely normal in French.

French often uses the singular possessive when each person has one thing of that kind.

So utiliser votre téléphone can mean:

• each of you may use your phone

English does something similar:

• Please raise your hand not usually
• Please raise your hands unless both hands are meant

If the speaker wanted to emphasize multiple phones, vos téléphones would also be possible, but votre téléphone sounds very natural here.

Aussi means also / too.

In:

• on vous autorise aussi à utiliser votre téléphone

it means that, in addition to being allowed to enter the room, you are also allowed to use your phone.

Its position is flexible in some cases, but here it naturally comes before à utiliser votre téléphone by being placed after the verb:

• on vous autorise aussi à utiliser votre téléphone

That placement makes it modify the whole permission idea: you are also allowed.

Yes. A native speaker might often say something simpler, for example:

• Vous pouvez entrer dans cette pièce et utiliser votre téléphone.
• Vous êtes autorisés à entrer dans cette pièce et à utiliser votre téléphone.
• On vous autorise à entrer dans cette pièce et à utiliser votre téléphone.

The original sentence is grammatically correct, but it is a little repetitive because it uses autoriser twice.

This may be deliberate if the speaker wants to emphasize both permissions separately.

Dans means in / inside, and cette pièce means this room.

So:

• entrer dans cette pièce = to enter this room

French uses entrer dans when you are talking about going into an enclosed space.

Examples:

• entrer dans la maison = enter the house
• entrer dans la salle = enter the room/hall
• entrer dans le bureau = enter the office

You may also hear entrer en classe in some set expressions, but entrer dans cette pièce is the normal, straightforward form here.

Not always. Pièce is a general word for room, especially a room inside a building or home.

But depending on context, French might also use:

• salle = room, hall, classroom, waiting room, etc.
• chambre = bedroom
• bureau = office
• salon = living room/lounge

So cette pièce is correct and general, but in real life the exact noun might change depending on what kind of room it is.

For example:

• dans cette salle might sound more natural for a classroom or meeting room
• dans cette chambre would mean a bedroom
• dans ce bureau would mean an office