Learn Hardcore Indonesian: Masalah kecil di kantor kami punya solusi cepat. - A small problem at our office has a quick solution.

mempunyai or memiliki: Masalah kecil di kantor kami memiliki solusi cepat.
A more neutral rewording with ada: Ada solusi cepat untuk masalah kecil di kantor kami.

Is bolded masalah kecil singular or plural? How do I make it explicit?

By default it’s ambiguous; context tells you whether it’s a small problem or small problems.

Explicit singular: sebuah masalah kecil or satu masalah kecil.
Explicit plural: masalah-masalah kecil, beberapa masalah kecil (some), berbagai masalah kecil (various). Note: para is not used with non-human nouns like masalah.

Should it be bolded kami or kita?

kami = we/us (excluding the listener). Good if you’re speaking to someone outside the office.
kita = we/us (including the listener). Use this if you’re talking to a colleague about your shared office. Example: Masalah kecil di kantor kita punya solusi cepat.

Why does the adjective bolded as kecil come after masalah?

Indonesian adjectives typically follow the noun: masalah kecil, solusi cepat. Prepositional phrases like di kantor kami also follow the noun phrase they modify.

Can I move bolded di kantor kami to the front for emphasis?

Yes: Di kantor kami, masalah kecil punya solusi cepat. Fronting the location is common for emphasis and doesn’t change the meaning.

Do I need bolded yang before punya?

No. yang would turn what follows into a modifier of the noun. Without yang, punya is the main verb.

Without yang (your sentence): statement about the whole subject.
With yang: Masalah kecil di kantor kami yang punya solusi cepat … implies you’re distinguishing which small problems (among others) have quick solutions.

Does bolded solusi cepat mean the problems are solved quickly? How do I say that idea?

solusi cepat means quick solutions (adjective + noun). If you want are solved quickly (adverbial idea), rephrase:

Masalah-masalah kecil di kantor kami biasanya cepat diatasi.
Masalah kecil di kantor kami cepat diselesaikan.
Masalah-masalah kecil di kantor kami cepat terselesaikan. Here cepat modifies the solving process, not the solution.

How do I express habit like usually or often?

Add adverbs:

biasanya = usually
sering = often Example: Masalah-masalah kecil di kantor kami biasanya punya solusi cepat.

Is bolded solusi good Indonesian? Any synonyms?

Yes, solusi is standard. Common alternatives:

jalan keluar (very common, neutral): Masalah kecil di kantor kami punya jalan keluar yang cepat.
penyelesaian (resolution): Penyelesaiannya cepat.
pemecahan exists but more often in the collocation pemecahan masalah (problem solving).

What’s the difference between bolded kecil and sedikit?

kecil = small/minor (size/degree): masalah kecil = minor problem.
sedikit = a little/few (quantity): sedikit masalah = a few problems.
They’re not interchangeable.

How do I negate this sentence?

Two common ways:

Negate the verb have: Masalah kecil di kantor kami tidak punya solusi cepat.
Say there is no solution for it: Tidak ada solusi cepat untuk masalah kecil di kantor kami.
The second is often more natural for there is no.

Is bolded di the right preposition? What about ke or pada? And what about spacing?

di = at/in (location): di kantor.
ke = to (direction).
pada is formal and used with abstract objects or certain set phrases; pada kantor is odd—use di kantor. Spacing:
Preposition di is written separately: di kantor.
Passive prefix di- attaches to verbs: diselesaikan, diatasi.

How do I show definiteness like the in the small problems?

Indonesian has no articles; context determines definiteness. To make it explicit:

Add itu after the noun phrase: Masalah-masalah kecil di kantor kami itu punya solusi cepat.
Use -nya to mark definiteness/possessive: Solusinya cepat.

Is there a more idiomatic way to phrase the same idea?

Depending on nuance:

With there is: Ada solusi cepat untuk masalah kecil di kantor kami.
Emphasizing resolution speed: Masalah-masalah kecil di kantor kami biasanya cepat diatasi/mudah diselesaikan. All are natural; choose based on whether you want to focus on having a solution or on the speed of resolving the problems.