Consobrinus dicit consobrinam melius cantare quam se, sed se clarius cantare.

The main clause is Consobrinus dicit = the male cousin says.

After dicit, Latin uses indirect statement, often called the accusative-and-infinitive construction. So the rest breaks into two reported statements:

• consobrinam melius cantare quam se
• sed se clarius cantare

So the sentence is basically:

• He says that she sings better than he does
• but that he sings more clearly

Because in Latin indirect statement, the subject of the reported statement goes into the accusative, and the verb goes into the infinitive.

So instead of a direct statement like:

• consobrina cantat = the female cousin sings

after dicit it becomes:

• consobrinam cantare = that the female cousin sings

That is why consobrinam is accusative.

For the same reason: after a verb like dicit (says), Latin commonly reports speech with an accusative + infinitive construction.

So:

• direct speech: Consobrina cantat
• indirect speech: dicit consobrinam cantare

And later:

• direct speech: Ego clarius canto
• indirect speech: dicit se clarius cantare

English usually uses that plus a normal finite verb, but Latin often uses this infinitive construction instead.

In both places, se refers back to consobrinus, the subject of dicit.

So:

• quam se = than he
• se clarius cantare = that he sings more clearly

This is a standard use of the reflexive pronoun in indirect statement: it points back to the speaker or thinker of the reported statement, here consobrinus.

Because this comparison is still inside indirect statement.

What is being compared is really:

• consobrinam melius cantare
• se cantare

In other words:

• that the female cousin sings better than he sings

Since the understood subject of the second half is also inside an accusative-and-infinitive construction, Latin uses se in the accusative, not a nominative form.

So quam se here really means than he does, with the infinitive cantare understood.

Yes. That is the most natural way to understand it.

The full sense is:

• consobrinam melius cantare quam se [cantare]

So literally:

• that the female cousin sings better than he sings

Latin often leaves out a repeated word when it is obvious from the context.

They are comparative adverbs.

• melius = better
• clarius = more clearly

They are adverbs because they describe how the singing is done, so they modify cantare, not a noun.

A useful detail:

• melius is the comparative adverb of bene (well)
• clarius is the comparative adverb of clare (clearly)

So:

• melius cantare = to sing better
• clarius cantare = to sing more clearly

Yes. The sentence is comparing different qualities of singing.

It says, in effect:

• she is better at singing overall
• but he is clearer in his singing

There is no contradiction. Latin, like English, can compare one person favorably in one way and the other person favorably in another way.

Because the first dicit can govern both infinitive clauses.

So Latin does not need to repeat it:

• Consobrinus dicit consobrinam melius cantare quam se, sed se clarius cantare.

The sense is:

• The male cousin says that the female cousin sings better than he does, but that he sings more clearly.

English often repeats less than beginners expect too, but Latin is especially comfortable letting one verb control multiple parallel phrases.

A natural direct-speech version would be:

• Consobrina melius cantat quam ego, sed ego clarius canto.

That helps show what changed in indirect speech:

• consobrina → consobrinam
• cantat → cantare
• ego → se
• canto → cantare

So the indirect statement is just the reported version of that direct statement.

The word order helps, but Latin word order is more flexible than English word order.

What matters most is the grammar of the forms:

• Consobrinus is nominative, so he is the subject of dicit
• consobrinam and se are accusative, so they are subjects of the infinitives in indirect statement
• melius and clarius modify cantare
• quam introduces the comparison

So even if the order feels unusual to an English speaker, the endings tell you how the sentence works.