Learn Hardcore Croatian: Doktor kaže da moramo smanjiti količinu soli u jelima. - The doctor says that we have to reduce the amount of salt in the dishes.

Context tells you whether it is specific or general.
So Doktor kaže… can be understood as The doctor says… or A doctor says…, depending on what was said before.

What is the role of da in kaže da moramo smanjiti…?

Here da is a conjunction meaning that, introducing a subordinate clause:

Doktor kaže da moramo smanjiti…
= The doctor says that we must reduce…

So the structure is:

Main clause: Doktor kaže
Subordinate clause: da moramo smanjiti količinu soli u jelima

It is similar to English say that / think that / know that, etc.

Could you say Doktor kaže moramo smanjiti… without da?

Technically, yes – you might hear:

Doktor kaže moramo smanjiti količinu soli u jelima.

But:

with da: it sounds more neutral, standard, and clear.
without da: it sounds more informal, a bit more like spoken language.

For learners and in most written contexts, it is safer and more natural to keep da:
Doktor kaže da moramo smanjiti…

Why is it moramo smanjiti and not something like moramo smanjujemo?

In Croatian, the modal verb morati (must, have to) is followed by an infinitive:

moramo smanjiti = we must reduce

So the pattern is:

moramo + infinitive:
moramo jesti, moramo spavati, moramo smanjiti

Using a finite verb after moramo (like smanjujemo) is incorrect in standard Croatian.
You cannot say moramo smanjujemo.

What does moramo express, and how is it different from trebamo or treba?

moramo (from morati) = we must / we have to
Strong obligation or necessity, often external (doctor, rules, health).
trebamo (from trebati) = we should / we need to
Often a bit weaker, can sound like recommendation or general need.
treba is impersonal:
Treba smanjiti količinu soli. = (One) needs to reduce the amount of salt. / The amount of salt needs to be reduced.

In your sentence, moramo fits very well because the doctor is giving a strong recommendation, almost an obligation.

Why is there no mi for we before moramo?

Croatian is a pro‑drop language: the subject pronoun is often omitted because the verb ending already shows the person and number.

mi moramo = we must (pronoun included, for emphasis or clarity)
moramo = we must (pronoun omitted, normal and default)

The ending ‑mo on moramo clearly indicates we (1st person plural), so mi is not necessary unless you want to stress we:

Mi moramo smanjiti… (We, in particular, must…)

What case is količinu and why is it used?

količinu is accusative singular of količina (amount, quantity).

It is the direct object of the verb smanjiti (to reduce):

smanjiti (što?) količinu
to reduce (what?) the amount

Direct objects of transitive verbs in Croatian are normally in the accusative case, which is why količina changes to količinu here.

Why is it soli and not just sol after količinu?

soli here is genitive singular of sol (salt).

Noun količina (amount) usually takes a genitive to show amount of something:

količina soli = amount of salt
količina vode = amount of water
količina šećera = amount of sugar

So the phrase količinu soli combines:

količinu – accusative (object of smanjiti)
soli – genitive (dependant on količina, showing of what)

What case is jelima and why isn’t it jela?

The noun jelo (dish, meal) is neuter. Its plural forms include:

nominative plural: jela (dishes, meals)
accusative plural: jela
dative / locative / instrumental plural: jelima

The preposition u can take:

locative = in a place (static): u jelima – in dishes
accusative = into a place (movement): u jela – into the dishes

In your sentence, the meaning is in dishes (no movement), so u jelima (locative plural) is correct, not u jela.

What aspect is smanjiti, and is there also smanjivati?

Yes, Croatian verbs have aspect.

smanjiti – perfective: to reduce (as a single, completed action or as a result)
smanjivati – imperfective: to be reducing, to keep reducing (ongoing, repeated)

In a sentence like:

Doktor kaže da moramo smanjiti količinu soli…

the perfective smanjiti is natural because the focus is on achieving a result (getting the amount of salt down from now on), not on the ongoing process itself.

You might see moramo smanjivati if the emphasis is on continually lowering or repeatedly reducing over time, but for general advice/result, smanjiti is more typical.

Can the word order change, for example: Doktor kaže da količinu soli moramo smanjiti u jelima?

Yes, Croatian word order is quite flexible, and your example is grammatically correct:

Doktor kaže da količinu soli moramo smanjiti u jelima.

Different orders change emphasis, not basic meaning:

da moramo smanjiti količinu soli u jelima – neutral, very common
da količinu soli moramo smanjiti u jelima – slight emphasis on količinu soli (it’s specifically the amount of salt we must reduce)

All of these are understandable; the version you were given is the most neutral and typical.