Haec persona veritatem aperte fatetur.

Because haec has to agree with persona in gender, number, and case.

• persona is a feminine singular nominative noun
• so the demonstrative this must also be feminine singular nominative
• that form is haec

The three nominative singular forms are:

• hic = this (masculine)
• haec = this (feminine)
• hoc = this (neuter)

So haec persona means this person.

Not necessarily. In Latin, persona is a grammatically feminine noun, so words agreeing with it must be feminine too, even if the actual person could be male.

So in this sentence:

• haec is feminine because persona is feminine
• but the real-life person being talked about does not have to be a woman

This is a very common thing in Latin: grammatical gender and natural gender are not always the same.

Persona is nominative singular.

You can tell because it is the subject of the sentence: it is the one doing the action of fatetur.

So the structure is:

• haec persona = the subject, this person
• veritatem = the object, the truth
• aperte fatetur = openly admits/confesses

Because it is the direct object of fatetur.

The verb fatetur means admits, confesses, or acknowledges, and the thing being admitted is put in the accusative:

• veritas = truth
• veritatem = truth, as a direct object

So veritatem fatetur means admits the truth.

Aperte is an adverb. It means openly, plainly, or frankly.

It describes how the person admits the truth.

Compare:

• apertus, aperta, apertum = open (adjective)
• aperte = openly (adverb)

So:

• persona veritatem fatetur = the person admits the truth
• persona veritatem aperte fatetur = the person openly admits the truth

Because fateor, fatēri, fassus sum is a deponent verb.

A deponent verb:

• has passive-looking forms
• but an active meaning

So fatetur looks like a passive form, but it means:

• he/she admits
• not he/she is admitted

This is one of the most important things to learn about Latin verbs: some verbs are passive in form but active in meaning.

Fatetur is:

• 3rd person singular
• present tense
• indicative mood
• from the deponent verb fateor, fatēri

So it means:

• he admits
• she admits
• it admits

In this sentence, since the subject is haec persona, the natural translation is this person admits.

Yes. Even though it has passive-looking forms, it behaves according to its active meaning.

Since fatetur means admits/confesses, it can take a direct object in the accusative:

• veritatem fatetur = admits the truth

So you should translate by meaning, not by the appearance of the ending.

Yes, haec can sometimes mean these, but not here.

That is because haec has multiple possible forms in the demonstrative paradigm. In this sentence, we know it is feminine singular nominative because it agrees with persona, which is singular.

So here:

• haec persona = this person

If it were plural, the noun would also be plural.

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

This sentence is fairly straightforward:

• Haec persona = subject
• veritatem = object
• aperte fatetur = adverb + verb

But Latin could rearrange the words for emphasis. For example:

• Veritatem haec persona aperte fatetur
• Aperte haec persona veritatem fatetur

These would still mean roughly the same thing, though the emphasis might change.

The given order is natural and clear.

It can cover all of those ideas, depending on context.

Common possibilities are:

• admits
• confesses
• acknowledges

The basic idea is that someone owns up to or states openly something as true.

Since the sentence also includes aperte (openly), the sense is especially close to:

• openly admits the truth
• frankly confesses the truth

So the exact English choice depends on the tone of the translation you want.