Ostajem ovde zauvek.

Because Serbian often drops subject pronouns when they are already clear from the verb ending.

Ostajem ends in -m, which tells you the subject is I. So Ostajem ovde zauvek is perfectly complete without ja.

You can add ja for emphasis or contrast:

• Ja ostajem ovde zauvek. = I’m staying here forever.

That can sound more emphatic, as if contrasting with someone else.

The base form is ostajati, which is an imperfective verb.

So:

• ostajati = to stay, to remain
• ostajem = I stay / I am staying / I’m remaining

In this sentence, ostajem is 1st person singular present tense.

Because ostajem and ostanem come from different aspects:

• ostajati → imperfective
• ostati → perfective

Ostajem is the natural choice when you describe an ongoing state or a decision that is in effect now.

Ostanem is the present form of the perfective verb ostati, but perfective present forms usually do not work like normal present tense in independent statements. So Ostanem ovde zauvek is not the normal way to say this.

A learner-friendly rule:

• use ostajem for I’m staying / I remain
• use ostaću for I will stay

Yes. It is grammatically present tense, but it describes a state that begins now and continues into the future.

This is similar to English sentences like:

• I’m staying here forever.

So the Serbian present tense here does not mean only right now. It can also express a present decision with future duration.

Yes, absolutely.

• Ostajem ovde zauvek. = I’m staying here forever.
• Ostaću ovde zauvek. = I will stay here forever.

The difference is mostly in perspective:

• ostajem sounds like a decision or state that is already happening now
• ostaću sounds more explicitly future

Both are natural, but ostajem can feel a bit more immediate and emotionally committed.

Ovde means here, usually near the speaker.

It is not exactly the same as tu:

• ovde = here, where I am
• tu = there / here near you / in that spot we both know

Also, ovde and ovdje are regional/standard variants:

• ovde = common Ekavian Serbian
• ovdje = Ijekavian variant

So a speaker using Ijekavian might say:

• Ostajem ovdje zauvijek.

That means the same thing.

Zauvek is an adverb meaning forever.

It does not change for case, gender, or number. It stays the same.

So in this sentence:

• ostajem = verb
• ovde = adverb of place
• zauvek = adverb of time/duration

You may also see the variant zauvijek, especially in Ijekavian.

Not much, because there are no nouns here.

This sentence is made of:

• a conjugated verb: ostajem
• an adverb of place: ovde
• an adverb of time: zauvek

Since ovde and zauvek are adverbs, they do not take case endings. The main grammar point here is the verb form, not noun cases.

Yes. Serbian word order is fairly flexible.

The given sentence is natural:

• Ostajem ovde zauvek.

But other orders are possible, with different emphasis:

• Ovde ostajem zauvek. → emphasizes here
• Zauvek ostajem ovde. → emphasizes forever
• Ja ostajem ovde zauvek. → emphasizes I

So the meaning stays basically the same, but the focus shifts.

The Serbian letter j is pronounced like English y in yes.

So:

• ostajem sounds roughly like OH-sta-yem
• ovde sounds roughly like OV-de

A few useful pronunciation points:

• Serbian spelling is quite phonetic
• every written letter is normally pronounced
• j is never like English j in job

So ostajem is not os-ta-jem with an English j sound; it is os-ta-yem.

Yes, it sounds natural, but it is quite strong and final.

Zauvek gives it a dramatic or decisive tone, like:

• a firm life decision
• an emotional declaration
• a line in a film, story, or argument

In everyday speech, people may often say simply Ostajem ovde unless they really want to stress the idea of forever.

So the sentence is natural, but it sounds more intense than a plain everyday statement.