Čak ni neispravna stvar nema trag korišćenja.

Čak ni means not even or even ... not, with strong emphasis.

So Čak ni neispravna stvar... means something like:

• Not even the faulty item...
• Even the faulty item doesn’t...

It highlights that the statement is true in an extreme case too.

In Serbian, this is normal. Serbian uses negative concord, which means multiple negative words appear together in the same clause.

So:

• ni = marks not even
• nema = does not have / there is no

This is not considered bad grammar in Serbian. In fact, it is the expected pattern.

Compare:

• Niko ništa ne zna. = Nobody knows anything.
  • literally: Nobody nothing doesn’t know

So Čak ni neispravna stvar nema... is structurally normal Serbian.

Neispravna is the feminine form of neispravan.

For objects, it usually means:

• faulty
• defective
• not working properly
• out of order

So here it does not mean morally wrong or incorrect in an abstract sense. It means the item is defective or not functioning properly.

Because it agrees with stvar, which is a feminine singular noun.

In Serbian, adjectives must match the noun in gender, number, and case.

Here:

• stvar = feminine singular
• so the adjective must also be feminine singular:
  • neispravna stvar

Compare:

• neispravan uređaj = a faulty device
• neispravna stvar = a faulty thing/item
• neispravno vozilo = a faulty vehicle

It is grammatically fine, but it is quite generic.

Stvar literally means thing, so in real-life product descriptions Serbian speakers might more naturally use a more specific word, such as:

• predmet = item/object
• artikl = item/article
• proizvod = product
• uređaj = device
• primerak = copy/unit

So neispravna stvar is understandable, but depending on context, it may sound a little vague.

Literally, it means a trace of use.

In more natural English, that is usually:

• a sign of use
• evidence of use
• wear marks
• signs of wear

This kind of phrase is common in descriptions of second-hand items.

Related expressions you may also see:

• tragovi korišćenja = signs/traces of use
• znaci korišćenja = signs of use
• tragovi upotrebe = traces/signs of use

Korišćenja is the genitive singular of korišćenje.

Here it depends on trag:

• trag čega?
• trag korišćenja
• a trace of what?
• a trace of use

So this is a very common Serbian pattern:

• miris dima = smell of smoke
• znak umora = sign of tiredness
• trag krvi = trace of blood
• trag korišćenja = trace/sign of use

Also, korišćenje is a verbal noun related to koristiti / to use.

In standard Serbian, this sounds off. You would normally expect:

• nema traga korišćenja or
• nema tragova korišćenja

After nema, Serbian very often uses the genitive for the thing that is absent.

So the more standard version would be:

• Čak ni neispravna stvar nema traga korišćenja. = Even the faulty item has no trace/sign of use.

Or, more naturally in many contexts:

• Čak ni neispravna stvar nema tragova korišćenja. = Even the faulty item has no signs of use.

So yes, a learner would be right to suspect that trag in the original sentence is probably a mistake or a nonstandard form.

Nema is the 3rd person singular present form of nemati = to not have.

Here the subject is singular:

• neispravna stvar = the faulty item/thing

So:

• stvar nema = the item does not have

If the subject were plural, you would use:

• nemaju = do not have

Example:

• Neispravne stvari nemaju tragove korišćenja.

Yes. Serbian word order is more flexible than English word order.

The version with Čak ni at the front gives strong emphasis:

• Čak ni neispravna stvar nema...
• Not even the faulty item has...

A less emphatic version could be:

• Neispravna stvar nema traga korišćenja.

You could also move things around for a different focus, for example:

• Tragova korišćenja nema ni na neispravnoj stvari.

That sounds more like:

• There are no signs of use even on the faulty item.

So the fronted čak ni neispravna stvar is mainly about emphasis.

A few natural possibilities are:

• Čak ni neispravna stvar nema traga korišćenja.
• Čak ni neispravna stvar nema tragova korišćenja.
• Čak ni neispravan predmet nema tragove korišćenja.
• Ni neispravan artikl ne pokazuje znakove korišćenja.

If this is about selling or describing a product, many speakers would prefer a more specific noun than stvar, such as predmet, artikl, or uređaj, depending on the object.