Sic discipuli, cum historias inter se comparent et testimonia personarum diligenter audiant, facilius intellegunt quid sit verum et quid falsum.

Here sic means something like thus, in this way, or so. It points forward to the method described in the cum clause:

• cum historias inter se comparent et testimonia personarum diligenter audiant
  = when/by comparing stories with one another and listening carefully to people’s testimony

So sic discipuli ... intellegunt means in this way the students understand more easily.

The main clause is:

• Sic discipuli ... facilius intellegunt

The subject is discipuli and the main verb is intellegunt.

Everything between the commas beginning with cum is a subordinate clause:

• cum historias inter se comparent et testimonia personarum diligenter audiant

And quid sit verum et quid falsum is another subordinate clause depending on intellegunt.

So the structure is:

• main statement: the students understand more easily
• circumstance/method: when/since/by comparing... and listening...
• indirect question: what is true and what is false

Because this is not just a simple time clause meaning when in a purely factual sense. With the subjunctive, cum often introduces a clause that gives the circumstance, background, cause, or general situation.

So:

• cum ... comparent et ... audiant

means something like:

• when, since, or as they compare... and listen...

The subjunctive makes it feel less like a one-time clock-time event and more like a general condition or circumstance under which the main action happens.

Both are present subjunctive active, 3rd person plural.

• comparent = they may compare / they compare in a subjunctive clause
• audiant = they may hear / they listen in a subjunctive clause

They are plural because the subject is discipuli.

Formation:

• comparo → present subjunctive comparent
• audio → present subjunctive audiant

Inter se means among themselves, with one another, or with each other.

So:

• historias inter se comparent

means they compare stories with one another or they compare the stories among themselves.

A very literal way to think of it is:

• inter = among/between
• se = themselves

This is a very common Latin expression.

Because comparent is a transitive verb here: they compare something. The thing being compared is the direct object, so it goes into the accusative.

• historias = stories as the direct object of comparent

So:

• historias comparent = they compare stories

Personarum is the genitive plural of persona. It means of persons/people.

So:

• testimonia personarum

literally means the testimonies of people or people’s testimony/testimonies.

The genitive shows possession or association. English often uses of or an apostrophe to express this idea.

Facilius is the comparative adverb of facile = easily.

So:

• facile = easily
• facilius = more easily

It modifies the verb intellegunt:

• facilius intellegunt = they understand more easily

This is adverbial, not adjectival, because it describes how they understand.

Because this is an indirect question after intellegunt.

Direct question:

• Quid est verum?
• Quid est falsum?

Indirect question:

• intellegunt quid sit verum et quid falsum
• they understand what is true and what is false

In Latin, indirect questions normally use the subjunctive, so est becomes sit.

Because quid here means what? in an indirect question.

• quid sit verum = what is true
• quid falsum = what is false

By contrast, quod often means because, which, or the fact that, depending on context. It would not be the normal word here for an indirect question.

So if the idea is what is true?, Latin naturally uses quid.

Because they are being used substantively, meaning the true thing and the false thing, or more naturally in English, what is true and what is false.

Latin often uses neuter singular adjectives this way to express an abstract idea:

• verum = what is true / the truth
• falsum = what is false / falsehood

That is why they are not masculine or feminine plural agreeing with historias or testimonia.

Most naturally here it means when, since, or as, depending on how you want to bring out the sense in English.

Because the sentence explains how the students come to understand better, since or when both work well:

• when they compare... and listen...
• since they compare... and listen...

It does not sound adversative here, so although would be unlikely.

Because intellegunt is the main assertion of the sentence: the students understand more easily. Latin normally uses the indicative in the main clause when stating a fact.

The subjunctives are inside subordinate clauses:

• comparent
• audiant
• sit

But the sentence’s central claim is presented as straightforward fact:

• discipuli facilius intellegunt

Yes. One cum introduces both verbs:

• cum historias inter se comparent et testimonia personarum diligenter audiant

So the sense is:

• when/since they compare stories with one another and listen carefully to people’s testimony

The et simply joins the two actions inside the same cum clause.

Diligenter is an adverb meaning carefully, attentively, or diligently.

It modifies audiant:

• testimonia personarum diligenter audiant
• they listen carefully to people’s testimony

So it tells you how they listen.