Danas u učionici nema nikoga; nitko ne želi raditi.

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).

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.

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.

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.

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.”

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.

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.

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.

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.

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.