Kad budeš blizu škole, nazovi me.

Because after kad referring to a future time, Croatian normally does not use the ordinary future with ću/ćeš/će.

So instead of something like Kad ćeš biti blizu škole..., Croatian uses kad budeš....

Here, budeš is the form used for you will be / you are in this kind of future time clause:

• Kad budeš blizu škole... = When you are near the school...

This is very natural and standard Croatian.

In form, budeš looks like a present-type form, but here it functions as part of what learners usually think of as a future meaning.

For practical learning, it is best to remember:

• after kad
  • future meaning, Croatian often uses budem, budeš, bude...
• so kad budeš means when you are / when you will be

With the verb biti (to be), this is the normal way to express that future idea in this structure.

Yes, but the meaning shifts.

• Kad budeš blizu škole, nazovi me.
  = When you get near the school / when you are near the school on a future occasion.

• Kad si blizu škole, nazovi me.
  = more like Whenever you are near the school, call me or a general repeated situation.

So if you are talking about one future moment, budeš is the better choice.

Škole is in the genitive singular.

That is because blizu normally takes the genitive:

• blizu kuće = near the house
• blizu grada = near the city
• blizu škole = near the school

The base form is škola.
After blizu, it changes to škole.

Good question. Škole can indeed be:

• genitive singular of škola
• or nominative plural

Here, the word blizu tells you what it must be. Since blizu requires the genitive, škole here must mean:

• of the school / near the school

So in this sentence it is singular, not plural.

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

So Croatian simply says:

• škola = school / a school / the school
• blizu škole = near a school / near the school

Context tells you which meaning is intended. In your sentence, the meaning is understood from the situation.

Nazovi is the imperative of nazvati, which is a perfective verb. It usually means call once, give me a call, or make sure you call.

That fits this sentence well, because the speaker wants one completed action:

• Kad budeš blizu škole, nazovi me.
  = When you’re near the school, call me.

By contrast, zovi me comes from zvati and is more imperfective. It can sound more like:

• call me repeatedly
• keep calling me
• call me in general

So nazovi me is the natural choice here.

Because nazvati takes a direct object, and the unstressed clitic form for me is me.

• nazovi me = call me

Here is the difference:

• me = unstressed me
• mene = stressed/emphatic me
• mi = to me / me in the dative, not used here

So:

• Nazovi me. = normal
• Nazovi mene. = emphatic, like Call me, not someone else
• Nazovi mi = incorrect here

Because me is a clitic, and Croatian clitics usually go in a special unstressed position near the beginning of their clause.

In an imperative clause like this, the natural order is:

• Nazovi me.

That is the normal, neutral order.
You would not usually say Me nazovi unless you were doing something marked or highly emphatic.

Yes, absolutely.

Both are natural:

• Kad budeš blizu škole, nazovi me.
• Nazovi me kad budeš blizu škole.

The difference is mainly in emphasis:

• starting with Kad budeš blizu škole highlights the time condition first
• starting with Nazovi me puts the command first

Both mean essentially the same thing.

Here kad means when.

It introduces a time clause:

• Kad budeš blizu škole... = When you are near the school...

It is not the same as ako, which means if.

Compare:

• Kad budeš blizu škole, nazovi me.
  = when you are near the school, call me

• Ako budeš blizu škole, nazovi me.
  = if you happen to be near the school, call me

So kad suggests the speaker expects that moment to happen, while ako is more conditional.

Because the sentence begins with a subordinate clause:

• Kad budeš blizu škole = dependent time clause
• nazovi me = main clause

When that dependent clause comes first, Croatian separates it from the main clause with a comma:

• Kad budeš blizu škole, nazovi me.

So the comma marks the boundary between the two parts of the sentence.