Iudex reae veniam dare potest, si veritatem tandem fatetur.

Because reae is dative singular here.

The phrase veniam dare alicui means to give pardon to someone or to grant someone forgiveness. Since the person receiving the pardon is an indirect object, Latin puts that noun in the dative.

• rea = an accused woman / female defendant
• reae = to the accused woman

So:

• Iudex reae veniam dare potest = The judge can give pardon to the accused woman

Veniam is accusative singular.

It is the direct object of dare (to give). The thing being given is the pardon, so Latin uses the accusative:

• venia = pardon, favor, forgiveness
• veniam = pardon / forgiveness as the direct object

So in the phrase:

• reae = to the accused woman (indirect object, dative)
• veniam = pardon (direct object, accusative)

Because it depends on potest.

Latin uses possum (can, am able) with an infinitive, just like English uses can with a bare verb:

• potest dare = can give

So:

• potest = is able / can
• dare = to give

Together they form the verbal idea can give.

Because fateor is a deponent verb.

A deponent verb has passive forms but an active meaning. So although fatetur looks like a passive form, it is translated actively:

• fatetur = he/she confesses, admits, acknowledges

Its dictionary form is:

• fateor, fatēri, fassus sum

So in this sentence, fatetur means she confesses or she admits.

Because it is the object of fatetur.

The verb fateor can take a direct object meaning admit/confess something:

• veritas = truth
• veritatem = truth as the direct object

So:

• veritatem fatetur = she confesses the truth / she admits the truth

Si means if and introduces a condition.

The clause

• si veritatem tandem fatetur

means

• if she finally confesses the truth

This is a straightforward, open condition in Latin, so the verb is in the indicative.

Because the sentence gives a general present-time possibility:

• The judge can grant the accused woman pardon, if she finally confesses the truth.

Latin often uses the present indicative in this kind of condition when the idea is real or open:

• if she confesses
• if she does confess

It is not expressing something contrary to fact or hypothetical in a remote sense; it is a normal condition.

Tandem means at last, finally, or eventually.

It modifies fatetur:

• veritatem tandem fatetur = she finally confesses the truth

Latin word order is flexible, so tandem can be placed where the writer wants emphasis or rhythm. Here it naturally highlights the idea that the confession comes at last.

Not exactly.

In Latin, reus/rea often means the accused person, defendant, or sometimes the guilty party, depending on context. In this sentence, reae most naturally means to the accused woman or to the female defendant.

So you should not automatically translate rea as guilty woman every time. Context matters.

Because iudex is in the nominative singular, which is the normal case for the subject.

• iudex = judge
• nominative singular = the judge as the doer of the action

The judge is the one who can grant pardon, so iudex is the subject of potest.

Latin word order is much more flexible than English because the endings show how words function.

Here the sentence is:

• Iudex reae veniam dare potest, si veritatem tandem fatetur.

A more English-like order would be something like:

• Iudex potest reae veniam dare...

But Latin can place words in different positions without changing the basic meaning, because:

• iudex is nominative
• reae is dative
• veniam is accusative
• dare is infinitive
• potest is the finite verb

So the endings, not just the position, tell you who is doing what.

Yes. Veniam dare literally means to give pardon or to grant forgiveness, and it is a normal Latin expression.

Depending on context, you might translate it in smoother English as:

• grant pardon
• forgive
• show mercy to

So although the literal wording is give pardon, the natural English translation may vary.

Yes, that is the natural understanding.

The sentence says:

• The judge can grant the accused woman pardon, if she finally confesses the truth.

Latin does not need to repeat she explicitly, because the verb ending in fatetur already tells you there is a third-person singular subject: he/she/it. From the context, that subject is understood to be the accused woman.

So reae in the main clause corresponds in sense to the understood she in the si-clause.