Ovaj okvir je star, ali lijep, pa ga želim sačuvati za portret moga djeda.

Croatian does not have articles like English the and a/an.

So okvir can mean frame, a frame, or the frame, depending on context. In this sentence, ovaj already makes it specific: ovaj okvir = this frame.

Because ovaj has to agree with okvir in gender, number, and case.

• okvir is masculine
• singular
• nominative here, because it is the subject of je star

So the correct form is ovaj.

Compare:

• ovaj okvir = this frame masculine
• ova slika = this picture feminine
• ovo staklo = this glass neuter

Here the adjectives are used predicatively, after the verb je:
okvir je star, ali lijep = the frame is old, but beautiful.

In this position, Croatian normally uses the forms star and lijep, agreeing with okvir:

• masculine
• singular
• nominative

So:

• okvir je star
• okvir je lijep

The forms stari and lijepi are not the normal choice in this kind of sentence.

It is understood from the verb form želim.

Croatian often leaves out subject pronouns when they are clear from the verb ending.
želim means I want.

So:

• želim = I want
• želiš = you want
• želi = he/she wants

You could say ja želim for emphasis, but it is not necessary.

Here pa works like so, and so, or therefore.

It links the two ideas:

• This frame is old, but beautiful
• so I want to preserve it

So pa shows a consequence or natural continuation.

It is very common in everyday Croatian and often sounds more natural than a heavier connector like zato.

Ga refers back to okvir: it.

It is the unstressed accusative pronoun form, equivalent to English him/it depending on context. Here it means it.

• ga = short, unstressed form
• njega = full, stressed form

In this sentence, there is no special emphasis, so Croatian uses the short form ga.

So:

• želim ga sačuvati = I want to preserve it
• želim njega sačuvati would sound emphasized, something like I want to preserve that one / him

Because ga is a clitic: a short unstressed word that usually goes in second position in its clause.

The clause begins with pa, so the clitic comes right after it:

• pa ga želim sačuvati

This word order is very typical in Croatian.

A learner might want to say pa želim ga sačuvati, but that is not the normal placement for the clitic here.

This is a question of aspect, which is very important in Croatian verbs.

• čuvati = imperfective, ongoing activity: to keep / to guard / to be preserving
• sačuvati = perfective, completed result: to preserve / to save / to keep safe successfully

In this sentence, the speaker means they want to preserve the frame for a purpose, with a clear result in mind. That is why sačuvati fits well.

So:

• želim ga sačuvati = I want to preserve it
• želim ga čuvati = I want to keep it / look after it

After za in this meaning, Croatian uses the accusative.

Here za portret means for a portrait or for use as a portrait frame.

The noun portret is masculine singular inanimate, and for that kind of noun, the nominative and accusative singular often look the same.

So:

• nominative: portret
• accusative: portret

That is why you do not see a visible change.

Because moga djeda is not the subject here. It is part of the phrase portret moga djeda = a portrait of my grandfather.

After a noun like portret, Croatian uses the genitive to show of:

• portret djeda = portrait of grandfather
• portret moga djeda = portrait of my grandfather

So both words change into the genitive:

• djed nominative becomes djeda genitive
• moj becomes moga or mojeg

So moga djeda is exactly what you expect after portret.

Yes, mojeg djeda is also possible.

In the genitive singular masculine, Croatian often allows both:

• moga
• mojeg

So both of these are acceptable:

• portret moga djeda
• portret mojeg djeda

In this sentence, moga djeda sounds completely natural.

Yes, you often could.

Croatian has the reflexive possessive svoj, which is commonly used when the possessor is the same as the subject.

Since the subject here is understood I from želim, svoga djeda can be very natural:

• želim sačuvati okvir za portret svoga djeda

That means I want to preserve the frame for a portrait of my own grandfather.

However, moga djeda is also understandable and natural here. Using svoj is often preferred when Croatian wants to make that same-subject relationship especially clear.