Thắt lưng và túi xách ở trên giá treo quần áo.

Thắt lưng means belt.

Literally:

• thắt = to tie / fasten
• lưng = back / waist area

But as a fixed expression, thắt lưng simply means belt.

Túi xách means handbag, purse, or sometimes bag carried by hand.

Parts:

• túi = bag
• xách = to carry by hand

So the literal idea is a bag you carry in your hand.

Và means and.

In this sentence, it joins the two nouns:

• thắt lưng = belt
• túi xách = handbag

So thắt lưng và túi xách = the belt and the handbag.

It works very much like English and.

Vietnamese often does not use a verb like English is/are in simple location sentences.

English:

• The belt and handbag are on the clothes rack.

Vietnamese:

• Thắt lưng và túi xách ở trên giá treo quần áo.

Here, ở gives the idea of to be located at / in / on. So Vietnamese does not need a separate are.

Ở trên means on, above, or up on, depending on context.

In this sentence, it means on:

• ở = at / located at
• trên = on / above

Together, ở trên emphasizes location: is/are on.

Yes, often you can.

Both are understandable:

• ở trên giá treo quần áo
• trên giá treo quần áo

The version with ở trên sounds a bit more explicitly locational, like located on.
The shorter trên is also common and natural in many contexts.

Giá treo quần áo means clothes rack or clothing rack.

Parts:

• giá = rack / stand / frame
• treo = to hang
• quần áo = clothes

So literally it is something like rack for hanging clothes.

Quần áo is a very common Vietnamese expression meaning clothes/clothing.

Originally:

• quần = pants
• áo = shirt/top/clothes

Together, quần áo means clothes in a general sense. Vietnamese nouns usually do not have a separate plural ending like English -s, so the plural idea comes from meaning and context, not word form.

Yes, the overall order is quite similar:

• Thắt lưng và túi xách = subject
• ở trên = location marker
• giá treo quần áo = place

So the pattern is roughly:

[thing] + [location expression] + [place]

That is close to English: [The thing] + is/are + [location]

Vietnamese usually does not require articles like English a/an/the.

So:

• thắt lưng can mean a belt or the belt
• túi xách can mean a handbag or the handbag

The exact meaning depends on context. If the meaning has already been shown to the learner, then here it is natural to understand them as specific items: the belt and the handbag.

Classifiers are common in Vietnamese, but they are not always required.

You often use classifiers when:

• counting things
• pointing things out
• emphasizing individual objects

For example:

• cái thắt lưng
• cái túi xách

But in a simple statement naming objects, classifiers are often omitted:

• Thắt lưng và túi xách ở trên giá treo quần áo.

So this sentence is natural without classifiers.

Yes. The sentence normally means that both items are on the clothes rack.

Because thắt lưng và túi xách is a single coordinated subject, the location phrase ở trên giá treo quần áo applies to both.

A rough English-friendly guide is:

thut luhng vah too-ee sahk uh chern zah treh-oh kwun ow

A few important notes:

• thắt has a short, clipped sound and a heavy falling/glottalized tone
• lưng has the ư vowel, which does not exist exactly in English
• túi sounds somewhat like too-ee
• xách in southern speech may sound a bit like sak, while northern speech keeps a clearer x sound
• ở has the vowel ơ, another sound not identical to English vowels
• quần áo is pronounced as two words, not as a single long one

If you want, I can also break the whole sentence down syllable by syllable with tone descriptions.

Yes, it is grammatical and natural.

It sounds like a normal descriptive sentence telling someone where things are. In everyday speech, a Vietnamese speaker might also slightly rephrase it depending on context, for example:

• Thắt lưng với túi xách ở trên giá treo quần áo.
• Thắt lưng và túi xách để trên giá treo quần áo.

But your sentence is perfectly fine.