Puer viam transire vult, sed mater eum monet ne sine ea transeat.

Because viam is the direct object of transire. In Latin, transeo, transire can take a direct object, so viam transire means to cross the road.

• via = road, street
• viam = the road (as the thing being crossed)

So Latin says literally the boy wants to cross the road.

Because it depends on vult. After verbs like volo (I want), Latin commonly uses an infinitive:

• vult transire = he wants to cross

This is very similar to English wants to cross, where to cross is also an infinitive.

Vult is the 3rd person singular present active indicative of volo, velle (to want).

So:

• volo = I want
• vis = you want
• vult = he/she wants

Here it agrees with puer, so puer ... vult = the boy wants.

Monet comes from moneo, monere, which can mean warn, advise, or remind, depending on context.

In this sentence, it means warns. Its structure is:

• mater eum monet = the mother warns him
• then a clause is added to say what she warns him not to do: ne sine ea transeat

So the full sense is: His mother warns him not to cross without her.

Because eum is the direct object of monet.

Latin often uses this pattern with moneo:

• someone warns someone
• the person warned is in the accusative

So:

• eum monet = she warns him

If it were ei, that would be dative (to him / for him), but that is not the construction used here.

Because ne is used to introduce a negative subordinate clause after verbs like warn, advise, fear, or in purpose-like clauses.

Here:

• ne transeat = that he not cross / not to cross

Latin does not say non transeat here, because this is not just a simple negation of a main verb. It is a dependent clause after monet.

So:

• mater eum monet ne ... transeat = his mother warns him not to cross...

Because it is in a subordinate clause introduced by ne after monet. After verbs of warning, Latin commonly uses ne + subjunctive.

So:

• transeat is present active subjunctive, 3rd person singular
• literally: that he may cross
• with ne: that he not cross

This is why Latin uses transeat, not an indicative form like transit.

Because the second part is not just another simple complement of a verb like vult. It is a full subordinate clause after monet:

• vult transire = wants to cross → verb + infinitive
• monet ne transeat = warns that he should not cross → verb + ne
  • subjunctive

So the two halves use different constructions:

1. volo + infinitive
2. moneo + ne + subjunctive

Ea is ablative singular feminine. It is ablative because it follows the preposition sine, which takes the ablative.

• sine = without
• ea = her

So:

• sine ea = without her

Because ea is a form of the pronoun is, ea, id (he, she, it / that), and here it refers back to mater, which is feminine.

Since mater is feminine singular, the pronoun referring to her is also feminine singular:

• mater = mother
• ea = her

And because it follows sine, it appears in the ablative:

• sine ea = without her

This is a very good question, because English learners often expect a reflexive pronoun here.

Latin uses se / secum only when the pronoun refers back to the subject of its own clause. But in ne sine ea transeat, the subject of transeat is the boy, not the mother.

So:

• subject of transeat = the boy
• ea refers to the mother

Since the pronoun does not refer to the subject of that clause, Latin uses the ordinary pronoun ea, not the reflexive se.

If Latin said sine se, it would mean without himself/herself, which is not the meaning here.

Because of the context and the construction.

The sentence begins with puer as the main subject, and then mater eum monet tells us that the mother warns him. The following clause ne sine ea transeat gives the action that he is being warned not to do.

So the understood subject of transeat is the same person as eum, namely the boy.

Latin often leaves such a subject unstated when it is easy to understand from context.

Yes: Latin word order is more flexible than English word order.

A very literal arrangement is:

• Puer = the boy
• viam transire vult = wants to cross the road
• sed = but
• mater eum monet = his mother warns him
• ne sine ea transeat = not to cross without her

Latin can move words around more freely because endings show their grammatical role. Here the order is quite natural and clear, but it is not as fixed as English.

Yes. Transire often means to cross or to go across, and with a direct object like viam it very naturally means cross the road.

So:

• viam transire = to cross the road
• literally, something like to go across the road

English usually prefers cross the road.

It has two main parts joined by sed (but):

1. Puer viam transire vult

   • main subject: puer
   • main verb: vult
   • infinitive complement: transire
   • object of the infinitive: viam

2. sed mater eum monet ne sine ea transeat

   • main subject: mater
   • main verb: monet
   • direct object: eum
   • subordinate clause: ne sine ea transeat

So the sentence combines:

• want + infinitive with
• warn + ne + subjunctive