Mặc dù modem mới, nhưng nó mất kết nối.

This is a very common concessive pattern in Vietnamese:

mặc dù ... nhưng ... = although ... (yet/but) ...

So:

• Mặc dù modem mới = although the modem is new
• nhưng nó mất kết nối = but it loses connection

Using both words together is natural and common. In everyday Vietnamese, people may also shorten it:

• Mặc dù modem mới, nó mất kết nối.
• Modem mới, nhưng nó mất kết nối.
• Dù modem mới, nhưng nó mất kết nối.

But the full pattern with both parts is very standard for learners to know.

Because Vietnamese often does not use a verb equivalent to English to be before adjectives.

So:

• modem mới here means the modem is new
• not literally new modem in this sentence’s function

This is very normal in Vietnamese. Compare:

• Nhà lớn. = The house is big.
• Máy tính cũ. = The computer is old.
• Modem mới. = The modem is new.

Learners often expect là, but là is usually not used before an adjective in this kind of sentence.

Usually no, or at least it would sound unnatural in this context.

Là is mainly used to link nouns or noun phrases, not adjectives:

• Anh ấy là bác sĩ. = He is a doctor.
• Đây là modem mới. = This is a new modem.

But when you want to say something is new / old / big / small, Vietnamese normally just uses the adjective directly:

• Modem mới.
• Modem cũ.
• Modem đắt.

So in your sentence, Mặc dù modem mới... is the natural pattern.

In Vietnamese, adjectives usually come after the noun they describe.

So:

• modem mới = new modem / the modem is new
• xe mới = new car
• điện thoại mới = new phone

That is the normal word order in Vietnamese.

One small extra point: in this sentence, modem mới is not just a noun phrase. Because it comes after mặc dù, it works like a shortened clause meaning although the modem is new.

No. Mới has several meanings in Vietnamese, and that often confuses learners.

Common meanings include:

• new
  
  • áo mới = new shirt
• just / only just / recently
  
  • Tôi mới ăn. = I just ate.
• sometimes part of time expressions or emphasis

In Mặc dù modem mới..., mới means new, not just.

Nó means it here, referring to the modem.

Vietnamese often repeats or restates the subject more than English does, especially when starting a new clause. So:

• Mặc dù modem mới, nhưng nó mất kết nối.

sounds natural because the second clause has its own clear subject: nó.

You could also repeat the noun:

• Mặc dù modem mới, nhưng modem vẫn mất kết nối.

That is grammatical, but repeating modem sounds a bit heavier.

If you remove nó completely:

• Mặc dù modem mới, nhưng mất kết nối.

this sounds less complete, because mất kết nối needs a clear subject.

No. For objects and animals, nó is a normal way to say it.

It can sound rude when used for a person, depending on context, but for things like a modem, it is fine.

So in this sentence:

• nó = it
• perfectly normal

Mất kết nối literally means lose connection or be disconnected.

In technology contexts, it can mean things like:

• losing internet connection
• losing network connection
• dropping a connection

Related expressions:

• bị mất kết nối = gets disconnected / is disconnected
  
  • adds a more passive sense
• mất mạng = loses internet / no internet
  
  • more casual, very common in speech
• ngắt kết nối = disconnect
  
  • often more deliberate, like actively disconnecting something

So nó mất kết nối means the modem loses connection.

It is understandable and basically grammatical, but many native speakers would probably say it a little differently for smoother, more natural Vietnamese.

Possible more natural versions:

• Mặc dù modem còn mới, nhưng nó vẫn mất kết nối.
• Mặc dù modem mới, nhưng nó vẫn bị mất kết nối.
• Dù modem còn mới, nó vẫn hay bị mất kết nối.

Why these may sound more natural:

• còn mới = still new
  This often sounds more idiomatic than just mới in a contrast like this.
• vẫn = still / nevertheless
  This helps emphasize the unexpected result.
• bị mất kết nối = gets disconnected
  Often natural in tech-related situations.

So your original sentence is understandable, but a native speaker might adjust it slightly.

The comma is common and helpful, especially because the sentence has two contrasting clauses:

• Mặc dù modem mới, nhưng nó mất kết nối.

It marks the pause after the concessive clause.

In casual writing, people may omit it:

• Mặc dù modem mới nhưng nó mất kết nối.

That is also fine. So the comma is not absolutely required, but it is natural and useful.

Yes. They are all common concessive words meaning something like although / though.

Examples:

• Dù modem mới, nhưng nó mất kết nối.
• Tuy modem mới, nhưng nó mất kết nối.
• Mặc dù modem mới, nhưng nó mất kết nối.

Very roughly:

• dù is shorter and common in speech
• tuy is also common
• mặc dù can sound a bit more formal or complete

All three are useful to recognize.