Si facultas adest, discipuli ad forum veniunt ut oratorem audiant.

It is a combination of:

• a conditional clause: Si facultas adest = if the opportunity is present / if there is an opportunity
• a main clause: discipuli ad forum veniunt = the students come to the forum
• a purpose clause: ut oratorem audiant = so that they may hear the speaker

So the structure is basically:

If X happens, the students do Y in order to do Z.

Adest comes from the compound verb adsum, adesse, which literally means to be present or to be at hand.

It is made from:

• ad- = to, near
• sum = I am

So adest means he/she/it is present or it is available.

In this sentence, the subject is facultas, which is singular, so the verb is also singular:

• facultas adest = the opportunity is present

Here facultas means something like:

• opportunity
• chance
• possibility

So Si facultas adest is a natural Latin way to say:

• If there is an opportunity
• If the chance presents itself
• If possible (loosely)

It does not mean faculty in the modern school/university sense here.

Discipuli is nominative plural, so it is the subject of veniunt.

You can parse it as:

• discipulus = student (singular)
• discipuli = students (nominative plural)

Since veniunt is they come, it matches discipuli perfectly.

Ad + accusative usually means to or toward a place.

So:

• ad forum = to the forum

This shows motion toward the forum.

If Latin wanted to say in the forum, it would normally use in foro instead. So the difference is:

• ad forum = to the forum
• in foro = in the forum

Forum is accusative singular.

That is because ad takes the accusative when it means movement toward something.

So:

• ad
  • accusative
• forum is the accusative singular form of forum

Therefore:

• ad forum = to the forum

Here ut introduces a purpose clause.

That means it explains why the students come to the forum:

• discipuli ad forum veniunt = the students come to the forum
• ut oratorem audiant = so that they may hear the speaker

So ut here means:

• so that
• in order that

It is not the same as every other use of ut. Latin ut can have several meanings, but here it clearly introduces purpose.

Because after ut in a purpose clause, Latin normally uses the subjunctive.

So:

• audiant = present subjunctive, 3rd person plural
• audiunt = present indicative, 3rd person plural

Latin uses the subjunctive here not because the action is doubtful, but because that is the standard grammar for a purpose clause:

• ut ... audiant = so that they may hear

This is one of the most important uses of the subjunctive in Latin.

Because oratorem is the direct object of audiant.

The verb audio takes a direct object in the accusative:

• audio oratorem = I hear the speaker

So here:

• audiant = they may hear
• oratorem = the speaker as the thing/person being heard

That is why it is accusative singular.

The form audiant is 3rd person plural, meaning they may hear.

The nearest and most logical plural subject is discipuli:

• discipuli ... veniunt ut ... audiant
• the students ... come so that ... they may hear

So the same people who come are also the ones who hear.

The sentence is describing a general or repeated situation:

• If the opportunity is there, the students come to the forum so that they may hear the speaker.

Latin often uses the present tense for this kind of general statement.

So:

• adest = is present
• veniunt = come
• audiant = may hear

This gives the sentence a sense like whenever there is an opportunity, this is what happens.

Latin word order is more flexible than English word order because the endings show the grammatical relationships.

So this sentence could be rearranged in different ways and still mean basically the same thing, as long as the forms stay clear.

For example, Latin could put ut oratorem audiant earlier or later for emphasis.

That said, the given order is quite natural:

• Si facultas adest first sets up the condition
• discipuli ad forum veniunt gives the main action
• ut oratorem audiant gives the purpose at the end

So even though Latin is flexible, this version is orderly and easy to follow.

Yes. Since it is a purpose clause, you can translate it in several natural English ways:

• so that they may hear the speaker
• in order to hear the speaker
• so they can hear the speaker

The first is the most literal to the Latin structure. The others are often more natural in English.

Yes, it is a very understandable and idiomatic kind of phrase.

Latin often expresses if possible or if the opportunity arises by using a noun like facultas with adest or similar verbs.

So Si facultas adest can feel slightly more formal or fuller than simple English if possible, but the idea is very natural:

• If the opportunity is available
• If the chance is there
• If circumstances allow

Yes:

• Si — if; introduces the conditional clause
• facultas — nominative singular; opportunity/chance
• adest — 3rd person singular present indicative of adsum; is present / is available
• discipuli — nominative plural; students
• ad — preposition taking the accusative; to, toward
• forum — accusative singular; forum
• veniunt — 3rd person plural present indicative of venio; they come
• ut — so that, introducing a purpose clause
• oratorem — accusative singular; speaker/orator
• audiant — 3rd person plural present subjunctive of audio; they may hear

That full parsing shows very clearly how the sentence is built.