Si servus verum dicit, iudex eum e carcere liberat.

Si means if. This is a basic conditional sentence:
if the slave tells the truth, then the judge frees him.

Both clauses use the indicative mood, so this is a straightforward, open condition, not a contrary-to-fact one.

They are both present indicative forms:

• dicit = he says / tells
• liberat = he frees

In a sentence with si, the present indicative often gives a general or straightforward condition: If X happens, Y happens. Depending on context, English may translate this as either:

• If the slave tells the truth, the judge frees him
• or sometimes If the slave tells the truth, the judge will free him

Latin itself here stays in the present.

Because both servus and iudex are in the nominative singular, the case normally used for the subject.

So:

• servus = subject of dicit
• iudex = subject of liberat

Also, each verb is third person singular, so each one needs a singular subject.

Verum is the neuter singular accusative form of verus, vera, verum (true), but here it is being used substantively—that is, as a noun-like word meaning the truth.

So verum dicit means he speaks/tells the truth.

This is a very common Latin pattern: a neuter adjective can be used as a noun.

Because verum here means the truth as a single idea.

• verum dicit = he tells the truth
• vera dicit would mean something more like he says true things

So the singular verum is the natural choice when the idea is truth in a general sense.

Because eum is the accusative singular masculine form of the pronoun is, ea, id.

That matters because liberat takes a direct object:

• iudex = the subject, the judge
• eum = the direct object, him

The nominative form is would mean he, not him. Since the judge is freeing him, Latin uses the accusative eum.

It refers back to servus.

We can tell because:

• servus is masculine singular
• eum is also masculine singular
• the sense of the sentence clearly fits: the judge frees the slave

So eum = him, meaning the slave.

The preposition e (or ex) means out of or from. With verbs like liberat, it can show what someone is being freed from.

So:

• e carcere = out of prison / from prison

This is a normal Latin way to express separation or movement out from something.

Because e/ex takes the ablative.

The noun is carcer, carceris (prison), and its ablative singular is carcere. So after e, Latin requires:

• e carcere

This is one of the standard jobs of the ablative: it is often used after prepositions that show place from which.

Yes. E and ex are two forms of the same preposition.

A common guideline is:

• e before consonants
• ex before vowels, and sometimes before consonants too

So e carcere is perfectly normal, and ex carcere would also be possible.

Yes, Latin word order is more flexible than English word order because the case endings show the grammatical roles.

This sentence begins with the if-clause:

• Si servus verum dicit = If the slave tells the truth

Then it gives the main clause:

• iudex eum e carcere liberat = the judge frees him from prison

That is a very natural order, but Latin could rearrange the words for emphasis. For example, eum could be moved, or e carcere could be placed earlier, without changing the basic meaning.

Because the verb endings already show the person and number.

• dicit = he/she/it says
• liberat = he/she/it frees

So Latin does not need to add a separate subject pronoun unless it wants emphasis or contrast. Instead, it just uses the nouns servus and iudex as the subjects.