Na računaru imam internet, ali na telefonu sada nemam internet.

In Serbian, devices are very often treated as something you are on, not in.

So:

• na računaru = on the computer
• na telefonu = on the phone

This is the natural way to talk about using a device or having something available on it.

Using u would usually sound like inside the computer/phone, which is a different idea.

So for internet access, na is the normal choice:

• Imam internet na telefonu.
• Nemam internet na računaru.

They are in the locative singular, because they come after na when it means a fixed location.

The basic forms are:

• računar = computer
• telefon = phone

After na, they become:

• na računaru
• na telefonu

For many masculine nouns, the dative and locative singular have the same form, often ending in -u, so learners often see the same ending in both cases.

Because imati (to have) has a special negative form in the present tense, written as one word:

• imam = I have
• nemam = I don't have

The full pattern is:

• imam
• imaš
• ima
• imamo
• imate
• imaju

Negative:

• nemam
• nemaš
• nema
• nemamo
• nemate
• nemaju

So nemam internet is the normal form, not ne imam internet.

Yes, literally it is I have internet, but in everyday Serbian that usually means:

• I have internet access
• I have an internet connection
• My internet works

This is a very common and natural way to say it.

If you want to be more explicit, you could say:

• Imam internet vezu. = I have an internet connection.
• Imam pristup internetu. = I have access to the internet.

But imam internet is perfectly normal in everyday speech.

Here, internet is the direct object of imam / nemam, so it is in the accusative.

However, internet is a masculine inanimate noun, and for that type of noun, the accusative singular is the same as the basic dictionary form.

So:

• dictionary form: internet
• accusative singular: internet

That is why you see:

• imam internet
• nemam internet

with no visible change.

Yes, it can be omitted if the meaning is clear.

Full version:

• Na računaru imam internet, ali na telefonu sada nemam internet.

Shorter version:

• Na računaru imam internet, ali na telefonu sada nemam.

Both are correct.

The repeated internet sounds a bit fuller and clearer, especially for emphasis or contrast. Omitting it is also natural when the object is obvious from context.

Sada means now or currently.

Serbian word order is more flexible than English word order, so adverbs like sada can move around more easily. In this sentence, putting sada before nemam highlights the current situation:

• na telefonu sada nemam internet = on the phone, I don't have internet now

Other possible word orders include:

• Ali sada na telefonu nemam internet.
• Ali na telefonu nemam internet sada.

They all mean roughly the same thing, but the original version sounds very natural and balanced.

Yes, it can.

Na telefonu can mean:

• on the phone device
• on the phone / in a phone conversation

Context tells you which one is meant.

For example:

• Pričam na telefonu. = I am talking on the phone.
• Na telefonu nemam internet. = I don't have internet on my phone.

In your sentence, because of the word internet, the meaning is clearly about the device, not a phone call.

Yes, both mean computer.

• računar is the more standard Serbian word
• kompjuter is also very common in everyday speech

So you may hear both:

• Na računaru imam internet.
• Na kompjuteru imam internet.

Both are natural. If you want the more standard/native-looking word, use računar.

Because Serbian does not have articles like English a/an/the.

So:

• računar can mean a computer or the computer
• telefon can mean a phone or the phone
• internet is understood from context

Serbian usually leaves definiteness to context. If needed, it can be made clearer with words like:

• ovaj = this
• taj = that
• jedan = one / a certain

But in your sentence, no article is needed.

Yes, you could, but the nuance changes a little.

• ali = but, stronger contrast
• a = often and/but/while, softer contrast or simple comparison

So:

• Na računaru imam internet, ali na telefonu sada nemam internet.
  Stronger contrast: I have internet on the computer, but not on the phone.

• Na računaru imam internet, a na telefonu sada nemam internet.
  Also correct, but slightly more neutral: I have internet on the computer, and/while on the phone I don't.

In this sentence, ali sounds very natural because the speaker is emphasizing the contrast.

A native speaker might shorten it in several ways, for example:

• Na računaru imam internet, ali na telefonu nemam.
• Na računaru imam internet, ali na telefonu sad nemam.
• Na kompu imam internet, ali na telefonu nemam.

A few notes:

• sad is a common spoken short form of sada
• komp is a casual spoken short form of kompjuter
• the second internet is often omitted if already understood

So the original sentence is fully correct, but in everyday speech it may be made shorter and lighter.