Park je dalje od moje kuće nego škola.

Because nego škola is a shortened comparison clause, not an od + genitive phrase.

The full idea is:

Park je dalje od moje kuće nego što je škola (od moje kuće).

So škola is really the subject of an implied clause, and subjects stay in the nominative.

If you used škole, it would suggest a different structure, and here it would sound wrong.

Because od requires the genitive case.

The basic form is:

• moja kuća = my house nominative

After od, it becomes:

• od moje kuće = from my house

Both words change because Serbian adjectives and possessives must agree with the noun in gender, number, and case.

They do two different jobs:

• od moje kuće = gives the reference point for distance: from my house
• nego škola = gives the second item in the comparison: than the school

So the sentence means roughly:

The park is farther from my house than the school is.

Dalje means farther / further away in this sentence.

It is the comparative form used in distance expressions such as:

• On živi dalje od mene. = He lives farther away than I do.
• Park je dalje od kuće. = The park is farther from the house.

So here dalje is the word that expresses the comparison in distance.

Because dalje is the form normally used for distance in a sentence like this.

• dalje = farther away
• dalji = further, later, more distant, usually when directly describing a noun

For example:

• dalji planovi = further plans
• u daljoj budućnosti = in the more distant future

But here we are not saying a farther park as an adjective before the noun. We are saying the park is farther away, so dalje is the natural form.

Yes. Serbian often leaves out repeated words when they are easy to understand.

The fuller version would be:

Park je dalje od moje kuće nego što je škola od moje kuće.

That is completely understandable, but it repeats od moje kuće, so Serbian normally shortens it.

Yes. That is a fuller and very clear version.

You could think of the versions like this:

• Park je dalje od moje kuće nego škola. = shorter, natural
• Park je dalje od moje kuće nego što je škola. = fuller, also natural
• Park je dalje od moje kuće nego što je škola od moje kuće. = fully explicit, but repetitive

Because Serbian does not have articles like a and the.

So park can mean a park or the park, depending on context.
The same is true for škola.

English needs articles, but Serbian usually does not.

No. They mean different things.

• nego škola = than the school
• nego od škole = than from the school

So:

• Park je dalje od moje kuće nego škola.
  = The park is farther from my house than the school is.

But:

• Park je dalje od moje kuće nego od škole.
  = The park is farther from my house than from the school.

That is a different comparison.

Yes, Serbian word order is fairly flexible.

The given order is natural and clear:

Park je dalje od moje kuće nego škola.

You may also hear slight variations, especially in speech, but the original version is a very good neutral model for learners. Serbian often moves parts of the sentence for emphasis, but the meaning here stays the same as long as the structure remains clear.