Mobilno bankarstvo radi na telefonu.

It literally means mobile banking.

• mobilno = mobile
• bankarstvo = banking as a service, field, or activity

This is a neuter singular noun phrase, so mobilno agrees with bankarstvo in gender, number, and case.

Because banka means bank as an institution or building, while bankarstvo means banking.

So:

• banka = a bank
• bankarstvo = banking

In this sentence, the subject is the service or function mobile banking, not the bank itself.

Here radi means works, functions, or runs.

It comes from the verb raditi, which often means:

• to work in the sense of having a job
• to function / operate
• to do in some contexts

In this sentence, it clearly means functions / works:

• Mobilno bankarstvo radi... = Mobile banking works...

Because the subject mobilno bankarstvo is grammatically singular.

Even though banking may feel like a general idea in English, in Serbian bankarstvo is a singular noun, so the verb must also be singular:

• bankarstvo radi = banking works

If the subject were plural, the verb would change too.

Because after na meaning on or on/in the context of a device, Serbian uses the locative case for location.

• dictionary form: telefon
• locative singular: telefonu

So:

• na telefonu = on the phone

If you used na telefon, that would sound wrong here because na + accusative usually suggests movement toward something, not location.

Not in this sentence.

Here na telefonu means on the phone/device, as in mobile banking works on a phone.

Depending on context, na telefonu can sometimes be understood as on the phone in a more general sense, but with mobilno bankarstvo the device meaning is the natural one.

If you wanted to say someone is speaking by phone, Serbian would usually express that differently depending on the exact idea.

In Serbian, na is often used for platforms, surfaces, devices, and places where something functions or appears.

So na telefonu is natural for on a phone or on the phone/device.

This is similar to other common expressions:

• na internetu = on the internet
• na ekranu = on the screen
• na telefonu = on the phone

English speakers often expect a direct one-to-one match with English prepositions, but Serbian prepositions do not always work exactly the same way.

Yes. Na mobilnom telefonu is perfectly correct and more explicit.

Compare:

• na telefonu = on the phone
• na mobilnom telefonu = on a mobile phone / cell phone

The original sentence is shorter and sounds natural if the context already makes it clear that a mobile phone is meant.

No, Serbian word order is fairly flexible.

The original order is neutral and natural:

• Mobilno bankarstvo radi na telefonu.

You could rearrange it for emphasis, for example:

• Na telefonu radi mobilno bankarstvo.

But that sounds more marked and would usually be used only if you want to emphasize na telefonu.

For learners, the original order is the safest and most neutral choice.

Because Serbian has no articles.

English uses:

• the phone
• a phone

Serbian usually leaves that unspecified unless the context makes it clear.

So telefonu can mean:

• the phone
• a phone
• phones, in a general sense, depending on context

That is normal in Serbian.

Not necessarily.

The sentence simply says that mobile banking works on the phone or can function on a phone. It does not automatically exclude other devices.

If Serbian wanted to stress only on the phone, it would usually add a word such as samo:

• Mobilno bankarstvo radi samo na telefonu. = Mobile banking works only on the phone.

So the original sentence is just a plain statement of compatibility or functionality.