Puer dicit ventum desiturum esse, sed mater id non credit.

Because it’s the subject of an indirect statement after dicit. In Latin, indirect statements typically use accusative + infinitive:

• puer dicit = the boy says (introduces reported speech)
• ventum ... esse = that the wind ... (wind becomes accusative as the reported subject)

It’s an indirect statement with a future infinitive built from:

• accusative subject: ventum (the wind)
• future active participle: desiturum (about to stop / going to stop)
• infinitive of esse: esse

Together, desiturum esse functions like to be going to stop / will stop.

Because it agrees with ventum in gender, number, and case:

• ventus (wind) is masculine, but in the accusative singular it ends in -um: ventum
• desiturus (future active participle) must match that form, so it becomes desiturum (masc. acc. sg.)

So it’s not neuter here; it just looks like the neuter because masculine accusative singular also ends in -um.

It’s a Latin way of expressing the future infinitive, which English usually expresses with a phrase. Depending on context, you might render it as:

• will stop
• is going to stop
• is about to stop

Latin forms this with future participle + esse rather than a single inflected infinitive.

Because in an indirect statement, Latin normally needs an infinitive to complete the reporting verb (dicit). The participle desiturum is not itself an infinitive; it’s a participle that needs esse to form the future infinitive:

• desiturum esse = to be going to stop (future infinitive)

Without esse, you’d have a participle without the infinitive structure the construction calls for.

Classical Latin strongly prefers accusative + infinitive after verbs of saying/thinking/knowing (dicit, putat, scit, etc.). Using a finite verb like desinet would be unusual in that role (more typical of some later Latin or special styles). So puer dicit ventum desiturum esse is the standard classical pattern.

dicit is present because the main clause is present: the boy says. The time of the reported action is shown inside the indirect statement:

• desiturum esse is future relative to dicit
  So it means: the boy says (now) that the wind will stop (after this).

sed means but and introduces a contrasting clause:

• puer dicit ... (the boy makes a claim)
• sed mater id non credit (but the mother doesn’t believe it)

It doesn’t force any special word order; it just signals contrast.

id is a neuter pronoun meaning it/that, referring to the entire idea the boy stated: that the wind will stop. Latin often uses id to avoid repeating the whole statement.

So:

• mater id non credit = the mother does not believe that (i.e., that claim)

Both are possible, but non commonly comes right before the verb or the element being negated. Here, non credit naturally groups as does not believe.
If you said non id credit, it could put a bit more focus on id (she doesn’t believe that—implying she might believe something else).

It can. credere has a few common patterns:

• credere + accusative = to believe something: id credit
• credere + dative = to believe someone / trust someone: puero credit (she believes the boy)
• credere + dative + accusative = to entrust something to someone

In this sentence, id is the thing believed (accusative).

Yes. mater is nominative because it’s the subject of the second main-clause verb credit:

• mater ... credit = the mother believes (or doesn’t believe)

So the sentence has two main clauses joined by sed: 1) puer dicit ...
2) mater id non credit