Learn Hardcore Croatian: Kako ćeš pisati hrvatski na poslu?

hrvatski here stands for “Croatian (language),” with the noun jezik (language) omitted.
It’s the direct object of pisati (to write), so it’s in the accusative. For inanimate masculine nouns/adjectives, the accusative form equals the nominative: hrvatski.
hrvatskog is genitive (or accusative animate), and hrvatskim is instrumental, so neither fits here.

Is pisati hrvatski the most natural way to say “write in Croatian,” or should I say pisati na hrvatskom?

Both are acceptable, but:

pisati na hrvatskom (“to write in Croatian”) is the most idiomatic in many contexts, especially when talking about the language used in writing.
pisati hrvatski is understood and feels more like “to write Croatian (as a skill/subject).”
A very formal variant is pisati hrvatskim jezikom (“to write by means of the Croatian language,” instrumental).

What exactly does na poslu mean, and what case is poslu?

na poslu = “at work/at the workplace.”
It’s na
- locative: static location uses na
  - locative.
The noun is posao; its locative singular is poslu.
Movement toward uses na
- accusative: na posao (“to work”).
u poslu means “in the middle of work” or “in business,” which is a different idea.

Can I change the word order? For example, can I move na poslu or hrvatski around?

Yes, Croatian allows flexible word order for nuance/emphasis, but keep the clitic ćeš in second position. Natural variants include:

Kako ćeš na poslu pisati hrvatski? (slight emphasis on the workplace)
Kako ćeš hrvatski pisati na poslu? (slight emphasis on the language) Avoid moving ćeš away from the second slot after Kako.

How do I make this sentence formal or address more than one person?

Use the plural/polite form ćete:

To one person formally or to several people: Kako ćete pisati hrvatski na poslu? You can include Vi for clarity/emphasis: Kako ćete Vi…

Can I add the pronoun ti (“you”)?

Yes, for emphasis or contrast:

Kako ćeš ti pisati hrvatski na poslu? (And how will YOU write Croatian at work?) Do not say Kako ti ćeš…—that misplaces the clitic. Keep ćeš immediately after Kako.

How do I make it negative?

Negation fuses with the auxiliary:

neću, nećeš, neće, nećemo, nećete, neće So the negative question is: Kako nećeš pisati hrvatski na poslu? (“How will you not write Croatian at work?”).
If you mean “Won’t you write…?” with a shade of surprise, you can say: Zar nećeš pisati hrvatski na poslu?

Why not use napisati instead of pisati?

pisati (imperfective) focuses on the process/habit (“to be writing,” “to write generally”).
napisati (perfective) focuses on a completed result (“to write and finish”).
Your sentence asks about manner in general, so pisati fits. You’d use napisati with a concrete, completable object:
Kako ćeš napisati izvještaj na hrvatskom? (How will you write/complete the report in Croatian?)

Why isn’t hrvatski capitalized?

Language names in Croatian are adjectives and are written in lowercase: hrvatski, engleski, njemački. In English, “Croatian” is capitalized, but in Croatian it isn’t (unless part of a proper name).

How do you pronounce ćeš, and what’s the difference between ć and č?

ćeš is pronounced roughly “chesh,” but with a softer “ch.”
ć is a softer, palatalized sound; č is a harder “ch” like in “church.”
š is like English “sh.”

Can the auxiliary come after the verb in the future?

In statements, yes, and when it does, you drop the final -i of the infinitive:

Pisat ću hrvatski na poslu. (not “Pisati ću”) However, after a question word like Kako, the clitic normally stays in second position:
Kako ćeš pisati…? is natural; placing ćeš after the verb here sounds wrong.

What are some natural ways to answer this question?

A few options (notice future placement and, when the auxiliary follows, dropping -i):

Na poslu ću pisati na hrvatskom.
Pisat ću e-mailove na hrvatskom.
Koristit ću hrvatsku tipkovnicu i provjeru pravopisa.
Pisat ću hrvatski u svim službenim porukama.