Learn Hardcore Croatian: Danas u učionici nema nikoga; nitko ne želi raditi. - Today there is nobody in the classroom; no one wants to work.

Ima means “there is / there are / (someone) has”.
Nema is simply ne + ima, so it means “there is not / there are not / (someone) does not have”.

In this sentence, nema nikoga literally means “there is nobody” (or “there isn’t anyone”).
Grammatically, nema is usually followed by the genitive case (here: nikoga, genitive of nitko).

Why is it nikoga in the first part, but nitko in the second part?

Nitko is the nominative form (the “dictionary form”) meaning “nobody / no one.”
Nikoga is the genitive form of the same word.

In nema nikoga, nikoga is in the genitive because nema (“there isn’t”) normally takes the genitive.
In nitko ne želi raditi, nitko is the subject of the sentence, and subjects are in the nominative.

So:

nitko = “nobody” as subject
nikoga = “nobody” after nema, in the genitive.

Why does Croatian use “double negatives” like nema nikoga and nitko ne želi? Isn’t that incorrect?

In Croatian, double negatives are normal and required; this is called negative concord.
When you have a negative verb (nema, ne želi) plus a negative pronoun (nikoga, nitko), you must keep both negatives.

So:

nema nikoga = “there is nobody / there isn’t anybody”
nitko ne želi raditi = “nobody wants to work”

If you said *ima nikoga or *nitko želi raditi, it would sound wrong or mean something different.
In English, double negatives usually cancel each other; in Croatian, they reinforce the negation.

Why is it u učionici, not u učionica?

The preposition u (“in”) can be followed by locative (location) or accusative (movement into).
Here, it describes location (“in the classroom”), so u takes the locative case.

Učionica (classroom) is feminine:

Nominative singular: učionica
Locative singular: učionici

So u učionici literally means “in (the) classroom” in the locative case.

Is the word order fixed? Could I say Danas nema nikoga u učionici instead?

Yes, Croatian word order is fairly flexible, and Danas nema nikoga u učionici is completely correct and natural.
The original sentence, Danas u učionici nema nikoga, puts a small emphasis on “in the classroom” as the place where nobody is.

All of these are possible and correct (with slightly different emphasis):

Danas u učionici nema nikoga.
Danas nema nikoga u učionici.
U učionici danas nema nikoga.

They all mean essentially: “Today there is nobody in the classroom.”

What is the difference between nitko and niko?

Both mean “nobody / no one,” but:

Nitko is the standard form in Croatian.
Niko is more typical in Serbian, Bosnian, and in some dialects; Croatians will understand it, but nitko is the standard Croatian form.

In standard Croatian you should use:

nitko (nominative)
nikoga (genitive), etc.

What does raditi mean here? Is it “to work” like a job, or “to do” something in general?

Raditi can mean both “to work (at a job)” and “to do, to work (on something)” depending on context.
In a school/classroom context, raditi usually means “to work (do schoolwork, exercises, tasks)”.

So nitko ne želi raditi here is best understood as:
“Nobody wants to work / do any work (in class).”
It doesn’t necessarily mean “nobody wants to go to their job”; it’s about not wanting to do tasks (homework, exercises, etc.) right now.

Could I say nitko ne želi učiti instead of nitko ne želi raditi?

Yes, but the meaning changes slightly.

Nitko ne želi raditi = “Nobody wants to work / do any work (tasks, exercises, activities).”
Nitko ne želi učiti = “Nobody wants to study / learn.”

Both are fine, but raditi is more general (“do work”), while učiti is specifically about studying/learning.

What tense is želi, and what verb is it from?

Želi is 3rd person singular, present tense of the verb željeti (“to want”).
So:

on/ona/ono želi = “he/she/it wants”
Here, the implied subject is nitko (“nobody”), so: nitko ne želi = “nobody wants.”

The full infinitive is željeti (with -jeti), but in speech and writing you’ll usually see present forms like želim, želiš, želi, želimo, želite, žele.

Why is there a semicolon (;) between the two parts? Could it be a period instead?

The semicolon in Danas u učionici nema nikoga; nitko ne želi raditi. separates two independent but closely related clauses.
It suggests: first, a fact (the classroom is empty), then the reason / explanation (nobody wants to work).

You could also write:

Danas u učionici nema nikoga. Nitko ne želi raditi. (two separate sentences), or
Danas u učionici nema nikoga, jer nitko ne želi raditi. (“…because nobody wants to work.”)

All are grammatically correct; the choice is mostly stylistic.