Puer exiturus matrem rogat utrum cum ea venire possit.

Exiturus is the future active participle of exire (to go out, leave).

Here it means something like about to leave or intending to leave. So puer exiturus means the boy, about to leave.

It is formed from the supine stem of exire:

• exire = to leave
• exitum = supine
• exiturus = about to leave / going to leave

So this participle shows an action that is still in the future relative to the main verb rogat.

Because it agrees with puer.

Puer is:

• masculine
• singular
• nominative

So the participle modifying it must also be:

• masculine
• singular
• nominative

That is why we get exiturus, not exitura or exiturum.

Because matrem is the direct object of rogat.

The verb rogare means to ask, and the person being asked is often put in the accusative:

• matrem rogat = he asks his mother

So here:

• puer = the one asking
• matrem = the person asked

This is a very common Latin pattern:

• rogat = he asks
• utrum ... possit = whether he can ...

So the whole structure is:

• he asks whether ...

This is an indirect question. In English, we often use whether or if. Latin here uses utrum.

Because utrum can introduce a simple yes/no indirect question all by itself.

So:

• rogat utrum venire possit = he asks whether he can come

If Latin gives two alternatives, then you often see:

• utrum ... an ... = whether ... or ...

But if only one side is stated, utrum alone is completely normal.

Because utrum cum ea venire possit is an indirect question, and Latin normally uses the subjunctive in indirect questions.

So:

• direct question: Possumne cum ea venire? = Can I come with her?
• indirect question: rogat utrum cum ea venire possit = he asks whether he can come with her

The form possit is the present subjunctive of posse.

It does not necessarily sound especially doubtful or hypothetical here; it is simply the normal mood for this construction.

Because the main verb is rogat (he asks), which is present, and the ability to come is happening at the same time as the asking.

So Latin uses the present subjunctive:

• rogat ... possit = he asks whether he can

This follows the normal sequence for indirect questions after a present-tense main verb.

The understood subject is puer.

Latin often leaves out subject pronouns when the subject is clear from the context. So in:

• utrum cum ea venire possit

the meaning is:

• whether he can come with her

That he is the boy, not the mother.

Because cum takes the ablative case.

So:

• ea = ablative singular feminine
• eam = accusative singular feminine

Since the preposition is cum, Latin must use ea:

• cum ea = with her

Because secum would refer back to the subject of the clause.

In the clause utrum cum ea venire possit, the understood subject is the boy. So:

• secum would mean with himself

But that is not the meaning here. The boy wants to come with his mother, so Latin uses:

• cum ea = with her

Here ea refers back to matrem.

Ea refers to matrem.

Both are feminine singular, so the connection is clear:

• matrem = mother
• ea = her

Latin often uses a pronoun like this instead of repeating the noun.

Because it depends on possit.

With verbs like possum, Latin regularly uses an infinitive to express the action someone is able to do:

• venire possit = can come

So:

• possit tells you about ability
• venire names the action

This is exactly the same basic idea as English can come.

Yes. Literally, venire means to come, but with cum ea it can naturally mean come with her or, in smoother English, go with her / accompany her, depending on context.

So an English translation may vary:

• come with her
• go with her
• accompany her

The Latin is not strange here; it is just one of those places where English may choose different wording.

It may look unusual if you expect English word order, but it is normal Latin.

The basic structure is:

• Puer = subject
• exiturus = participle describing the subject
• matrem rogat = main verb with object
• utrum cum ea venire possit = indirect question

Latin word order is more flexible than English because the endings show the grammatical relationships. So Latin can place words for emphasis or style without causing confusion.

A more mechanical English-style order would be something like:

• Puer matrem rogat utrum cum ea venire possit, exiturus but that is not how Latin naturally arranges it.

So the original order is perfectly good, and exiturus comes early because it closely describes puer.