Faber dicit tectum ante hiemem refectum iri.

Because Latin usually does not use a separate word like English that after verbs of saying, thinking, knowing, and so on.

Instead, it uses an indirect statement construction:

• dicit = says
• tectum ante hiemem refectum iri = that the roof will be repaired before winter

This construction is often called the accusative-and-infinitive construction.

Not exactly.

In this sentence, tectum is the subject of the infinitive refectum iri inside the indirect statement. Latin normally puts that subject into the accusative case.

So the structure is:

• Faber dicit = The workman says
• tectum ... refectum iri = the roof will be repaired

A helpful point: tectum is a neuter noun, and in neuter nouns the nominative and accusative singular look the same. So even though the form is tectum, its job here is accusative.

refectum iri is the future passive infinitive of reficio.

It means:

• more naturally in English: will be repaired
• more literally: to be going to be repaired

So the sentence is reporting a future action inside indirect statement.

It is the standard Latin future passive infinitive formation.

Traditional grammar describes it as:

• the supine in -um: refectum
• plus iri

So:

• refectum iri = to be going to be repaired

This is one of those forms that English does not match neatly with a single structure, so it is often best translated simply as will be repaired.

They are different kinds of words that just happen to look similar here:

• tectum is a noun meaning roof
• refectum is part of the verb phrase refectum iri

So they are not doing the same grammatical job.

This can feel confusing at first, but Latin often has forms that look alike while functioning differently.

Because reficietur would be a finite verb in a direct statement, while this sentence uses an indirect statement after dicit.

Compare:

• Tectum ante hiemem reficietur.
  The roof will be repaired before winter.

But after Faber dicit, Latin normally changes the reported verb into an infinitive:

• Faber dicit tectum ante hiemem refectum iri.
  The workman says that the roof will be repaired before winter.

hiemem is accusative singular.

It is accusative because the preposition ante takes the accusative. Here ante hiemem means before winter.

So:

• ante = before
• hiemem = accusative after ante

In normal understanding, it goes with refectum iri.

So the sense is:

• The workman says [the roof will be repaired before winter].

Not:

• Before winter, the workman says [the roof will be repaired].

Latin word order is flexible, but here the most natural reading is that before winter describes the time of the repairing.

The sentence does not say.

Because refectum iri is passive, Latin tells us what will happen to the roof, not who will do it.

If Latin wanted to name the agent, it could add an ab + ablative phrase, for example:

• ab fabro = by the workman
• ab operariis = by the workers

But in your sentence, the agent is simply left unstated.

Because the future passive infinitive in Latin is a special formation.

Compare:

• future active infinitive: refecturum esse = to be going to repair
• future passive infinitive: refectum iri = to be going to be repaired

So iri is just the normal element Latin uses in this construction. It is not something you should try to translate word-for-word every time; it is best learned as part of the whole pattern.

It is normal Latin word order.

Latin often puts:

1. the main clause first: Faber dicit
2. then the indirect statement
3. with the key verbal idea toward the end: refectum iri

English is more rigid about word order, but Latin is freer. So while the exact order can vary, this arrangement is very natural.