Ja najviše volim sveže voće.

Yes. Volim already tells you the subject is I, so ja is often omitted in Serbian.

• Volim sveže voće. = I like/love fresh fruit.
• Ja volim sveže voće. = the same basic meaning, but with extra emphasis on I

Including ja can sound more emphatic, contrastive, or simply a bit more explicit. In neutral speech, leaving it out is very common.

Here najviše means most or the most.

It is being used adverbially with volim, so the sentence means something like:

• I like fresh fruit the most
• Fresh fruit is what I like most

A useful comparison:

• mnogo = much / a lot
• više = more
• najviše = most

Serbian word order is flexible, but najviše volim is a very natural way to say I like ... the most.

So:

• Ja najviše volim sveže voće. = very natural
• Najviše volim sveže voće. = also very natural
• Sveže voće najviše volim. = possible, with extra emphasis on fresh fruit

If you put najviše elsewhere, the sentence may still be understandable, but this placement is the most standard and natural in a neutral statement.

Voće is the direct object of volim, so it is in the accusative case.

However, the form looks the same as the nominative. That is normal for many neuter singular nouns in Serbian: nominative and accusative are often identical.

So:

• nominative: voće
• accusative: voće

The case is different in function, even though the form does not change.

Because adjectives must agree with the noun they describe.

Here, voće is:

• neuter
• singular
• in the accusative case

So the adjective also takes the matching form: sveže.

Compare:

• svež hleb = fresh bread
• sveža jabuka = fresh apple
• sveže voće = fresh fruit

Because voće is often used as a collective or mass noun, just like English fruit can be.

So voće in the singular does not mean just one fruit item. It can mean fruit in general as a category.

That is why sveže voće naturally means fresh fruit, not necessarily one fresh fruit.

It can mean either, depending on context.

With food, hobbies, and general preferences, voleti is often translated as either like or love in English. The exact choice depends on how strong you want the English to sound.

So:

• Volim sveže voće can be I like fresh fruit or I love fresh fruit
• Najviše volim sveže voće = I like/love fresh fruit the most

With people, voleti often sounds stronger and is more likely to mean love.

Usually not with voleti in this sentence.

• najviše volim = I like/love ... the most
• najradije is more like most willingly / preferably

So Serbian normally says:

• Najviše volim sveže voće.

But najradije works well with actions, for example:

• Najradije jedem sveže voće. = I prefer eating fresh fruit / I most like to eat fresh fruit

So najviše is the better choice here.

Yes. That depends on the pronunciation standard being used.

• sveže = Ekavian
• svježe = Ijekavian

Both mean fresh. If you are learning standard Serbian as commonly used in Serbia, sveže is the usual form.