Learn Hardcore Croatian: U torbici nosim jednu novčanicu od dvadeset za kusur. - In my purse I carry one twenty banknote for change.

torbica = nominative (dictionary form)
u torbici = locative singular (in the little bag/purse)
If you meant movement into the purse, you’d use accusative: Stavljam je u torbicu (I put it into the purse).

What does torbica mean exactly, and how is it different from torba?

torba is a general bag (could be a handbag, shoulder bag, school bag, etc.).
torbica is a diminutive and often means a small bag/pouch/purse—something smaller and more “personal,” like a small handbag or a little pouch inside a bag. In everyday speech, torbica can correspond to what an English speaker might call a purse (depending on region/context).

Why is it nosim here? Does it mean “I wear” or “I carry”?

nositi can mean both to wear (clothes) and to carry (on you/with you). Here it means to carry (on me / with me):

Nosim jaknu. = I’m wearing a jacket.
Nosim novčanicu. = I’m carrying a banknote (on me).

Why is it jednu novčanicu and not jedan novčanik?

Because the word is novčanica (banknote), which is feminine, so the number one must agree:

feminine accusative: jednu novčanicu
Also, novčanik is a different word: it means wallet (masculine).

What case is novčanicu, and why is it in that case?

novčanicu is accusative singular (feminine). It’s in the accusative because it’s the direct object of nosim (I carry what? → novčanicu).
Base form: novčanica (nom.) → novčanicu (acc.).

What does od dvadeset mean literally? Why not just dvadeset?

Literally, novčanica od dvadeset means a banknote of twenty (a 20-unit bill). Croatian commonly uses od + number to express the denomination/value of a note or coin:

novčanica od deset = a ten-unit bill
kovanica od dvije kune = a 2-kuna coin (example with currency stated)

Why isn’t the currency (kuna/euro) mentioned after dvadeset?

It can be omitted when it’s obvious from context. In real life people often just say:

novčanica od dvadeset = a twenty (bill)
If you want to be explicit, you can add the currency:
novčanicu od dvadeset eura (or kuna, depending on context/time).

What does za kusur mean, and is kusur a formal word?

za kusur means for change / to have change (i.e., so you can receive or give small change).
kusur is very common in everyday speech. It’s not rude; it’s just colloquial/neutral, used a lot in shopping/payment contexts.

Why is it za kusur (with za)—what case does that take?

Here za means for (the purpose of), and it normally takes the accusative.
In practice, kusur often looks the same in nominative and accusative (depending on how you analyze its declension in modern usage), so learners mainly memorize the fixed phrase za kusur = for change.

Could the word order change? For example, Nosim u torbici... or Jednu novčanicu... nosim...?

Yes. Croatian word order is relatively flexible because endings show grammatical roles. Different orders shift emphasis:

U torbici nosim jednu novčanicu od dvadeset za kusur. (neutral: sets the scene first)
Nosim u torbici jednu novčanicu... (slightly more “I carry…” focused)
Jednu novčanicu od dvadeset nosim u torbici... (emphasizes what you carry)

Is torbici definitely singular? How would it look in plural?

Yes, torbici here is locative singular. Plural would be:

u torbicama = in (the) little bags/purses (locative plural)

How would you say “I keep” instead of “I carry” in this sentence?

A common alternative is držim (I keep/hold) if you mean it stays there:

U torbici držim jednu novčanicu od dvadeset za kusur.
Nosim emphasizes having it with you, while držim can emphasize it being stored/kept there.