Pater dicit fidem sine veritate manere non posse.

Because after dicit Latin often uses an indirect statement construction, also called the accusative and infinitive.

So instead of saying:

• Pater dicit quod fides manere non potest
  = Father says that faith cannot remain

Latin more classically says:

• Pater dicit fidem ... non posse
  literally, Father says faith ... not to be able

In this construction:

• the subject of the reported statement goes into the accusative → fidem
• the verb of the reported statement goes into the infinitive → posse

So fidem is accusative because it is the subject of the infinitive posse inside the indirect statement.

Because the reported statement is being expressed through an infinitive construction.

The core reported idea is:

• fides manere non potest
  = faith cannot remain

When this becomes indirect after dicit, it changes to:

• fidem manere non posse

Here:

• posse = to be able
• manere = to remain

Since posse normally takes another infinitive in Latin, manere stays as an infinitive too.

So the structure is:

• dicit = says
• fidem ... non posse = that faith is not able
• manere = to remain

Altogether: Father says that faith cannot remain without truth.

Because non posse means to be unable or cannot.

That is different from posse non, which means something more like to be able not to.

Compare:

• non posse manere = not to be able to remain / cannot remain
• posse non manere = to be able not to remain

So in this sentence, non posse is exactly what Latin uses to express cannot.

Because the preposition sine always takes the ablative case.

So:

• sine veritate = without truth

This is just a standard prepositional phrase:

• sine
  • ablative

Other examples:

• sine amico = without a friend
• sine spe = without hope
• sine pace = without peace

So veritate is ablative because sine requires it.

It goes most naturally with manere.

So the sense is:

• faith cannot remain without truth

In other words, the phrase describes the condition under which the remaining would happen: faith cannot continue or endure if truth is absent.

It is not really describing fidem by itself as if it meant faith without truth as a noun phrase. Instead, it modifies the verbal idea manere.

Manere basically means to remain, to stay, to continue, or sometimes to endure.

In this sentence, it means something like:

• to remain
• to continue to exist
• to endure

So fidem sine veritate manere non posse means that faith cannot last or continue without truth.

Because classical Latin usually does not need a separate word like English that in this kind of sentence.

English says:

• Father says that faith cannot remain without truth.

Latin usually says:

• Pater dicit fidem sine veritate manere non posse.

The idea of English that is built into the accusative and infinitive construction itself. So there is no need for a separate conjunction.

Because dico in this kind of sentence introduces an indirect statement, and the accusative noun before the infinitive is normally the subject of that indirect statement.

So the pattern is:

• dicit
• accusative subject
• infinitive verb

That means:

• fidem = subject of the reported statement
• posse = verb of the reported statement

If fidem were the direct object of dicit, the sentence would need a different structure and would not make good sense with the following infinitives.

Dicit is simply the present tense: he says or the father says.

So the main clause is happening in the present:

• Pater dicit = Father says

Then the present infinitives manere and posse show action that is contemporaneous with that main verb, meaning the statement is presented as true at the same time:

• Father says that faith cannot remain

So the time relationship is straightforward: the saying is present, and the inability to remain is also presented as current or generally true.

Because the statement is being presented as true at the same time as dicit.

• posse is the infinitive corresponding to potest
• manere is the infinitive corresponding to manet

If the direct statement were:

• Fides sine veritate manere non potest

then after dicit it naturally becomes:

• fidem sine veritate manere non posse

So the present infinitives preserve the idea that the statement is simultaneous with the main verb.

Yes, but it is normal Latin word order.

Latin often puts the main verb early and leaves the infinitive clause afterward:

• Pater dicit | fidem sine veritate manere non posse

Within the indirect statement, the words are arranged quite naturally:

• fidem = subject of the infinitive clause
• sine veritate = modifying manere
• manere = complementary infinitive
• non posse = main infinitive idea, cannot

Latin word order is more flexible than English, so the sentence could be rearranged without changing the basic grammar, but this version is clear and idiomatic.