Learn Hardcore Croatian: Treba im pomoć.

Because the verb agrees with the subject, not with the dative pronoun. In Treba im pomoć, the subject is pomoć (“help”), which is singular, so the verb is singular: treba. If the thing needed were plural, you’d use plural agreement:

Trebaju im stolice. = They need chairs.
Treba im stolica. = They need a chair.

What does im mean, and what form is it?

im is the unstressed dative plural clitic of “they,” meaning “to them.” It marks the experiencer/beneficiary with verbs like trebati in this pattern.

Other dative clitics:

mi = to me
ti = to you (singular)
mu = to him
joj = to her
nam = to us
vam = to you (plural)
im = to them

Example swaps:

Treba mi pomoć. = I need help.
Treba ti pomoć. = You need help.
Treba mu/joj pomoć. = He/She needs help.

What case is pomoć here, and why?

In Treba im pomoć, pomoć is nominative singular because it’s the grammatical subject (“help is needed”). With the personal construction, Trebam pomoć (“I need help”), pomoć is the direct object in the accusative, but its form happens to be identical to the nominative (many feminine nouns ending in a consonant don’t change form in acc. sg.). With other nouns you’ll see the difference:

Impersonal: Treba mi voda. (nominative subject)
Personal: Trebam vodu. (accusative object)

Can I start the sentence with im (e.g., Im treba pomoć)?

No. Clitics like im cannot stand first; they are second-position clitics and must come after the first stressed element. Good alternatives:

Treba im pomoć.
Pomoć im treba.
Njima treba pomoć. (using the full stressed form njima for emphasis)

Are there other natural ways to say the same thing?

Yes:

Oni trebaju pomoć. (personal verb; emphasizes “they”)
Njima treba pomoć. (focus on “to them”)
Potrebna im je pomoć. (literally “Help is necessary to them”; more formal/neutral)

What’s the difference between Treba im pomoć and Oni trebaju pomoć?

Both mean “They need help.” The impersonal style (Treba im pomoć) highlights the thing needed and uses a dative experiencer. The personal style (Oni trebaju pomoć) highlights the subject “they.” In everyday Croatian, both are fine; choice depends on emphasis and style.

How do I make it a yes/no question?

With the particle li (formal/neutral): Treba li im pomoć?
With intonation only (colloquial): Treba im pomoć? (rising intonation)

How do I negate it?

Put ne before the verb:

Ne treba im pomoć. = They don’t need help.
With plural subject: Ne trebaju im stolice. You can add emphasis:
Više im ne treba pomoć. = They no longer need help.
Ne treba im nikakva pomoć. = They need no help at all.

Why is it sometimes treba and sometimes trebaju?

Agreement is with the subject (the thing needed):

Singular subject: Treba im pomoć.
Plural subject: Trebaju im stolice.

What’s the difference between pomoć and pomoći?

pomoć (with ć) is the noun “help.”
pomoći (with ći) is the infinitive of the verb “to help” (perfective), and also a different noun form in some cases. Compare:
Treba im pomoć. = They need help. (noun)
Treba im pomoći. = It is necessary to help them / They need to be helped. (verb infinitive)

How do I say it in the past?

Agree the past participle of trebati with the subject (the thing needed):

Trebala im je pomoć. = They needed help. (subject pomoć, feminine sg.)
Trebali su im stolovi. = They needed tables. (plural subject) If there’s no noun subject (just an infinitive/clause), you’ll often see neuter:
Trebalo im je otići. = They needed to leave.

Where can I put the clitic im?

It must be in second position in the clause, after the first stressed element:

Sada im treba pomoć. (after Sada)
Pomoć im sada treba. (after Pomoć)
Not allowed: Im sada treba pomoć. (clitic first)

Can I replace im with njima?

Yes, for emphasis or when you don’t want a clitic:

Njima treba pomoć. You generally don’t use both together in standard Croatian (no clitic doubling in this case).

Why is there no article before pomoć?

Croatian has no articles. pomoć on its own can mean “help”/“some help.” Context supplies definiteness, or you can specify with adjectives: ta pomoć (that help), ikakva pomoć (any help), hitna pomoć (urgent help).

With mass nouns like “water,” do I say voda or vode after treba?

Both occur, with a nuance:

Treba mi voda. = I need water (as a resource, generic).
Treba mi vode. = I need some water (partitive feel). Your original sentence uses a countable abstract noun (pomoć), so it stays nominative: Treba im pomoć.