Pekara je bliže školi nego prodavnica.

Because Serbian often expresses to through a case ending rather than a separate word.

Here, škola becomes školi, which is the dative singular. After bliže (closer), Serbian commonly uses the dative for the thing something is closer to:

• škola = school
• školi = to the school

So bliže školi means closer to the school.

A useful comparison:

• blizu škole = near the school
• bliže školi = closer to the school

Because prodavnica is the subject of an implied second clause.

The sentence is basically:

Pekara je bliže školi nego prodavnica (je).

In English: The bakery is closer to the school than the store (is).

Since prodavnica is the subject of that understood clause, it stays in the nominative form: prodavnica.

If you said prodavnici, that would suggest a different meaning: than to the store.

No, Serbian makes the meaning clearer through case.

English The bakery is closer to the school than the store can mean either:

1. the bakery is closer to the school than the store is, or
2. the bakery is closer to the school than to the store

In Serbian:

• nego prodavnica = than the store is
• nego prodavnici = than to the store

So the sentence you gave means the first one.

Because here bliže is used as an invariable comparative form meaning closer. In this pattern, it does not change to match the gender of pekara.

So even though pekara is feminine, bliže stays bliže.

This is a common thing that confuses English speakers, because it looks like it should agree like an adjective, but in this construction it does not.

Nego means than in comparisons.

Here it introduces the second part of the comparison:

• Pekara je bliže školi nego prodavnica.
• The bakery is closer to the school than the store is.

So nego connects the bakery and the store as the two things being compared.

Sometimes yes, but the structure changes.

• nego is very natural here because what follows is really a shortened clause:
  nego prodavnica (je)

• nego što is used when you keep more of the clause:
  Pekara je bliže školi nego što je prodavnica.

• With od, the noun after it would go into the genitive:
  od prodavnice

So nego is a very good choice in your sentence because it clearly matches the meaning than the store is.

Because Serbian often omits repeated words when the meaning is obvious.

The full idea is:

Pekara je bliže školi nego prodavnica je bliže školi.

But that sounds repetitive, so Serbian normally shortens it to:

Pekara je bliže školi nego prodavnica.

English does something similar:

The bakery is closer to the school than the store (is).

Because Serbian does not have articles like English a and the.

So:

• pekara can mean a bakery or the bakery
• škola can mean a school or the school
• prodavnica can mean a store or the store

The exact meaning comes from the context. In this sentence, English naturally translates them as the bakery, the school, and the store.

Not completely. Serbian word order is fairly flexible because case endings show the grammatical relationships.

The given sentence is a normal, neutral way to say it:

Pekara je bliže školi nego prodavnica.

You may also hear other orders for emphasis, but for a learner, the version you have is the safest and most straightforward one.