Puer a matre veniam petit, quia mendacium dixit.

• Puer is nominative singular: it is the subject, the boy.
• a matre contains matre, which is ablative singular of mater: it shows the person from whom he seeks pardon.
• veniam is accusative singular of venia: it is the direct object of petit, the thing he asks for.
• mendacium is accusative singular: it is the direct object of dixit, the thing he said.

So the sentence uses two different object patterns:

• petere aliquid ab aliquo = to seek/ask something from someone
• dicere aliquid = to say something

Because Latin commonly says:

• aliquid petere ab aliquo = to ask/seek something from someone

So:

• veniam = the thing requested
• a matre = the person from whom it is requested

If you used matrem, that would make mother look like a direct object, which is not what the sentence means.

Both a and ab mean from. Before a consonant, Latin often uses a:

• a matre
• ab amico

So a matre is the normal form here because matre begins with m. You may sometimes see ab before consonants too, but a matre is the expected classical wording.

Petere is a very flexible verb. Its basic idea is something like aim at, seek, or go after, and from that it gets different meanings in different contexts.

Common meanings include:

• to seek
• to ask for
• to aim at
• sometimes to attack

In this sentence, because the object is veniam (pardon/forgiveness), veniam petit naturally means he asks for pardon or he seeks forgiveness.

So this is a good example of how Latin verbs often have a core meaning that shifts depending on context.

Because venia usually means favor, indulgence, pardon, or forgiveness as an abstract or mass-like idea, not a countable item.

So Latin says:

• veniam petere = to ask for pardon / forgiveness

English usually also treats this the same way:

• we say ask forgiveness or ask for pardon, not normally ask for pardons

Because Latin can say mendacium dicere, literally to say a lie, meaning to tell a lie.

That is perfectly idiomatic Latin:

• verum dicere = to say what is true
• mendacium dicere = to tell a lie

So mendacium is accusative because it is the direct object of dixit.

• petit is present tense: he asks / he is asking
• dixit is perfect tense: he said / he has said

The difference shows the time relationship:

• first, the boy told a lie
• now, as a result, he asks for pardon

So Latin uses:

• present for the main action happening now
• perfect for the earlier completed action

That is very natural Latin.

Because quia usually introduces a straightforward reason or fact:

• quia mendacium dixit = because he told a lie

When the reason is presented as an ordinary fact, Latin normally uses the indicative:

• dixit, not a subjunctive form

A learner often notices that Latin sometimes uses the subjunctive in causal clauses, but with quia and a simple factual reason, the indicative is the normal choice.

Because Latin verb endings usually show the subject clearly enough.

• petit = he/she/it asks
• dixit = he/she/it said

Since puer is already the subject, Latin does not need to add a separate pronoun like he. In fact, Latin often leaves subject pronouns out unless they are needed for emphasis or contrast.

No. Latin word order is much freer than English word order because the case endings show what each word is doing.

This sentence could be rearranged in several ways without changing the basic meaning, for example:

• Puer veniam a matre petit, quia mendacium dixit.
• Quia mendacium dixit, puer a matre veniam petit.

The version you were given is perfectly natural. Latin word order often helps with emphasis, rhythm, or style more than basic grammar.

Yes. Depending on context, it could be translated as:

• asks for pardon
• seeks forgiveness
• begs forgiveness
  if the context is more emotional

The Latin itself does not force only one English wording. Venia and petere together express the idea of trying to obtain pardon, and English can phrase that in different natural ways.

Because mater is a third-declension noun, and after a/ab it must be in the ablative.

Its forms include:

• nominative: mater = mother
• ablative: matre = from/by/with the mother, depending on context

Here it is:

• a matre = from the mother

So the change from mater to matre is just the normal case change required by the preposition.

In many contexts, yes: both quia and quod can mean because.

So a learner may see:

• quia mendacium dixit
• quod mendacium dixit

Both can introduce a causal clause. There can be stylistic and contextual differences in Latin authors, but for a beginner, it is enough to understand that both can mean because.