Learn Hardcore Latin: Discipuli bellum timent, sed pacem sperant. - The students fear war, but they hope for peace.

Discipuli is nominative plural of discipulus, -i (student/pupil).
In Latin, the subject of a finite verb is typically in the nominative case. Since both verbs (timent, sperant) are plural, discipuli naturally matches as their subject: the students.

How do we know timent means they fear (and not I fear, you fear, etc.)?

Because the verb ending tells you the person and number:

timent = 3rd person plural present active indicative of timēre
So it means they fear.

Likewise:

sperant = 3rd person plural present active indicative of spērāre = they hope (for)

Why are bellum and pacem in the accusative case?

Both are direct objects of their verbs:

timent takes a direct object: they fear (what?) → bellum
sperant takes a direct object: they hope for (what?) → pacem

In Latin, the direct object is typically accusative.

Why is bellum bellum (ending in -um) but pacem ends in -em?

They belong to different declensions and genders:

bellum, -i is 2nd declension neuter. Neuter accusative singular is the same as nominative singular, so it’s bellum.
pax, pacis is 3rd declension feminine. Its accusative singular is pacem.

So the endings reflect their declension patterns, not a difference in meaning.

Does bellum here mean a war or the war?

Latin has no definite or indefinite articles (no the/a).
So bellum could be translated as war, a war, or the war, depending on context. The same is true for pacem (peace / the peace).

What is the role of sed?

Sed is a coordinating conjunction meaning but.
It links two independent clauses:

Discipuli bellum timent
(dis) pacem sperant
So it marks a contrast: fear vs. hope.

Why isn’t the subject repeated in the second half (why not discipuli ... sed discipuli ...)?

Latin often omits repeated words when they are understood from context.
Since discipuli already clearly supplies the subject, the second clause simply continues with the new verb and object: sed pacem sperant = but (they) hope for peace.

Is Latin word order flexible here? Could this sentence be rearranged?

Yes. Latin word order is relatively flexible because case endings show grammatical roles. For example, these are still grammatical:

Bellum discipuli timent, sed pacem sperant.
Discipuli timent bellum, sed sperant pacem.

However, the original order is very natural: subject + object + verb, then contrast, then object + verb (with the subject understood).

What tense are timent and sperant, and does Latin need a helper verb like do?

Both are present tense. Latin does not use a helper like English do in statements.
So timent directly means they fear / they are fearing, and sperant means they hope / they are hoping (depending on context).

Does sperāre literally mean to hope for, and do I need a preposition like for in Latin?

In this construction, spērāre commonly takes a direct object in the accusative without a preposition.
So pacem sperant literally is they hope peace, which idiomatically becomes they hope for peace in English.

Why is there a comma before sed?

In English-style punctuation (often used in Latin textbooks), a comma is commonly placed before sed when it connects two independent clauses with contrasting ideas.
Ancient Latin manuscripts didn’t use punctuation like modern printed texts do, but modern editions add it for clarity.

How would I look up the dictionary forms of the nouns here?

You typically identify the nominative singular and genitive singular:

discipuli → dictionary entry discipulus, -i (nom. sg. discipulus)
bellum → bellum, -i
pacem → comes from pax, pacis (you can recognize the stem pac- in pacem)