Korisnička podrška radi danas.

It is a normal adjective + noun phrase:

• korisnička = customer / user-related
• podrška = support

So korisnička podrška is literally something like user support, but in natural English it usually means customer support or customer service.

Grammatically, podrška is the main noun, and korisnička describes it.

Because it has to agree with podrška.

In Serbian, adjectives change their form to match the noun in:

• gender
• number
• case

Here, podrška is:

• feminine
• singular
• nominative

So the adjective also takes the feminine singular nominative form: korisnička.

It is in the nominative case, because it is the subject of the sentence.

The subject is the thing doing the action, and here the action is radi.

So:

• korisnička podrška = subject
• radi = verb
• danas = adverb of time

Radi is the 3rd person singular present tense of raditi.

Here it means:

• works
• is working
• is operating
• sometimes even is open / is available, depending on context

With something like customer support, radi often means that the service is functioning or available.

Because Serbian does not need one here.

The verb radi already carries the whole verbal meaning. English often uses is working, but Serbian can simply use the present tense of the main verb:

• radi

So Serbian does not say something like is works or add another helper verb here.

It can mean either, depending on context.

Serbian present tense often covers both:

• habitual meaning: works
• current / temporary meaning: is working

In this sentence, danas strongly suggests a current or temporary situation, so the natural English meaning is often is working today, is available today, or is open today.

Danas means today.

It is an adverb of time, so it tells you when the action happens.

It does not change form here, and it applies to the whole statement:

• Korisnička podrška radi danas. = Customer support is working today.

Yes, it could go somewhere else.

Serbian word order is more flexible than English. The version you have is perfectly normal, but these are also possible:

• Danas korisnička podrška radi.
• Korisnička podrška danas radi.

The difference is mostly about emphasis and style, not basic meaning.

A rough guide:

• Danas korisnička podrška radi. → emphasizes today
• Korisnička podrška danas radi. → very natural, neutral
• Korisnička podrška radi danas. → also natural, slightly more focus on the time at the end

Because Serbian has no articles like English a/an/the.

So korisnička podrška can mean:

• customer support
• the customer support
• sometimes just support

The exact meaning depends on context.

The special letters are important:

• č sounds roughly like ch in chocolate, but a bit firmer
• š sounds like sh in shoe

So:

• korisnička → roughly ko-ris-nich-ka
• podrška → roughly pod-rsh-ka

A rough full pronunciation is:

ko-ris-nich-ka pod-rsh-ka ra-di da-nas

Yes, very often.

In Serbian, raditi can be used for:

• people → He works
• machines → The printer works
• businesses/services/offices → The office is open / operating
• systems → The site is working

So in this sentence, radi sounds very natural with customer support.

Yes, that is possible, but the nuance may be a little different.

• korisnička podrška = customer support, support service
• korisnička služba = customer service / customer service department

Both can work, but korisnička podrška is especially common when talking about support availability, especially in business or technical contexts.