Learn Hardcore Vietnamese: Trong phòng có một cái bàn sạch.

So here có does not mean to have/possess (as in Tôi có một cái bàn = I have a table), but rather introduces the existence of something in a place, just like English there is.

Why does the sentence start with Trong phòng instead of putting the place at the end like in English?

Vietnamese commonly puts the location at the beginning of an existential sentence to set the topic (what we are talking about) first:

Trong phòng có một cái bàn sạch.
→ Topic: Trong phòng (In the room)
→ Comment: có một cái bàn sạch (there is a clean table)

You can also say:

Có một cái bàn sạch trong phòng.

Both are correct.

Trong phòng có ... emphasizes the room.
Có một cái bàn sạch trong phòng emphasizes the existence of a clean table, then adds the location.

What is the function of một here? Is it like a / one in English, and can I leave it out?

Một literally means one, but very often it works like the English a / an (indefinite article):

một cái bàn sạch → a clean table / one clean table

Can it be omitted?

If you say Trong phòng có cái bàn sạch, it usually sounds like you are talking about a specific/known clean table (more like the clean table), not introducing a new one.
If you want to introduce an indefinite new object (like English There is a clean table in the room), một is the most natural choice.

So in this context, keeping một makes the sentence sound natural and indefinite, like English a.

What is cái and why do I need it before bàn?

Cái is a classifier (also called a measure word). Vietnamese typically needs a classifier when you:

count a noun
use a numeral like một before a countable noun

For objects like tables, chairs, books, etc., cái is a very common and neutral classifier.

Structure here is:

một (numeral)
cái (classifier)
bàn (noun)

So một cái bàn is the normal, correct way to say one table / a table.
Một bàn is not standard in careful speech; learners should keep the classifier.

Why is it bàn sạch and not sạch bàn? In English we say clean table (adjective before noun).

In Vietnamese, adjectives usually come after the noun they modify:

bàn sạch → table clean → a clean table
người cao → person tall → a tall person
nhà mới → house new → a new house

So the pattern is:

classifier + noun + adjective
- một cái bàn sạch
- một ngôi nhà đẹp (a beautiful house)

English: adjective + noun
Vietnamese: noun + adjective.

Does sạch here mean clean like just washed, or tidy/neat?

Sạch generally means clean, not dirty, free from dirt, dust, or stains.

For a table (bàn), bàn sạch usually implies it has been wiped, there is no dust or stains.
For a room: phòng sạch = the room is clean.

If you want to sound slightly more colloquial/emphatic, you might also hear:

bàn sạch sẽ
→ also clean, often with a slightly stronger or more vivid feel.

In this sentence, bàn sạch is completely natural and just means a clean table.

Is there a subject in Trong phòng có một cái bàn sạch? It looks like the sentence has no subject.

In Vietnamese existential sentences with có, there is often no explicit grammatical subject in the same way as in English:

English: There is a clean table in the room. (there acts as a dummy subject)
Vietnamese: Trong phòng có một cái bàn sạch.

You can think of the pattern as:

[Location] + có + [thing that exists]

The location (Trong phòng) works like the topic. The idea that a clean table exists there is expressed by có một cái bàn sạch, without needing a dummy subject like there.

Why don’t we use là (the to be verb) in this sentence?

Là is mainly used to link two noun phrases (or a pronoun and a noun phrase), like:

Anh ấy là giáo viên. → He is a teacher.
Đây là cái bàn. → This is a table.

With adjectives, Vietnamese normally does not use là:

Cái bàn sạch. → The table is clean. (no là)
Phòng này rộng. → This room is spacious.

In your sentence, có is the main verb (existence), and sạch is just an adjective describing bàn:

Trong phòng (location)
có (exist/existential verb)
một cái bàn (noun phrase)
sạch (adjective modifying bàn)

So there is no place for là here.

What is the difference between Trong phòng có một cái bàn sạch and something like Cái bàn trong phòng sạch?

They have different structures and typical uses:

Trong phòng có một cái bàn sạch.
- Existential: In the room, there is a clean table.
- Introduces a new object that exists in that location.
Cái bàn trong phòng sạch. (more natural: Cái bàn trong phòng thì sạch.)
- Descriptive: The table in the room is clean.
- Cái bàn trong phòng is a specific table (the one in the room), and the sentence is describing its state.

So:

Use Trong phòng có ... when you want to say there is/are ... in the room.
Use Cái bàn trong phòng (thì) sạch. when you already know the table and are saying it is clean.

Can I say Trong phòng có một cái bàn rất sạch or rất là sạch? How does that change the sentence?

Yes:

Trong phòng có một cái bàn rất sạch.
→ There is a very clean table in the room.

Here rất means very, and it modifies sạch.

You will also hear:

rất là sạch in spoken Vietnamese, e.g. cái bàn rất là sạch.

In careful, standard grammar, rất sạch is enough and slightly more neutral; rất là sạch is common and natural in everyday speech, especially to add emphasis.

Is Ở trong phòng có một cái bàn sạch also correct? What is the difference between trong and ở trong?

Yes, Ở trong phòng có một cái bàn sạch is also correct.

trong phòng = in the room
ở trong phòng = (located) in the room

Ở is a general preposition/verb for to be located at/in. Often:

At the beginning of the sentence, trong phòng and ở trong phòng are both fine.
Ở trong can sound a bit more explicit about location, but the meaning is the same here.

In many contexts, native speakers simply drop ở and just say trong phòng.

How would I say There are clean tables in the room (plural)? Do I have to change this sentence?

You can keep almost the same structure; Vietnamese often does not change the noun form for plural:

Trong phòng có những cái bàn sạch.
→ explicitly plural (with những, meaning some / indicating plural)

or simply:

Trong phòng có mấy cái bàn sạch. (if you mean a few clean tables)

Without những / mấy / vài / nhiều, the bare sentence:

Trong phòng có cái bàn sạch.

usually sounds singular and specific (more like the clean table), so to clearly express plural clean tables, use a plural marker like những, mấy, vài, nhiều, depending on what you want to say.

How are the tones pronounced in this sentence?

Word by word with tone names (Northern description):

Trong – no tone mark → mid-level tone
phòng – phòng with huyền (falling) → phòng
có – sắc (rising) → có
một – nặng (heavy, glottal stop at the end) → một
cái – sắc (rising) → cái
bàn – huyền (falling) → bàn
sạch – nặng (heavy, short/abrupt) → sạch

Practising slowly with clear tone and final consonants (ng, t, n, ch) will help the whole sentence sound natural.