Mater unam cepam et paulum allii emit.

Because cepam is the direct object of emit.

• cepa is the nominative singular form, the form you would use for the subject
• cepam is the accusative singular form, used for a direct object

Since the mother is buying the onion, onion is receiving the action, so Latin uses the accusative: cepam.

Because unam has to agree with cepam in gender, number, and case.

• cepa is feminine
• it is singular
• here it is accusative

So unus, una, unum must appear in the matching form, which is unam.

Because after paulum, Latin normally uses the partitive genitive.

So:

• paulum = a little bit
• allii = of garlic

Together, paulum allii literally means a little bit of garlic.

If Latin used allium here, it would not express that partitive idea in the normal classical way.

Here paulum means a small amount or a little bit.

It is a neuter singular form being used almost like a noun. So the phrase works like this:

• paulum = a little amount
• allii = of garlic

The whole phrase paulum allii is one object of emit.

Latin does not have articles like a, an, or the.

That means Latin often just uses a bare noun where English would need an article. So cepam by itself could often correspond to an onion or the onion, depending on context.

Here unam literally means one. Sometimes that matches English an, but it still has a numeric force. It can emphasize that the mother bought one onion.

Yes. Mater cepam et paulum allii emit would also be a perfectly possible sentence.

The difference is that:

• cepam = onion, with no explicit number stated
• unam cepam = one onion

So adding unam makes the quantity more explicit.

Without macrons, it is ambiguous in writing.

It could be:

• emit = buys
• ēmit = bought

If a text does not mark vowel length, both appear as emit. So you need the context, or the given translation, to know which one is meant.

Because mater is a third-declension noun, and third-declension nominative singular forms are often less predictable than first- or second-declension ones.

Here mater is the subject, so it is nominative singular. Its dictionary form is mater, and that is exactly the form used here.

In other cases you can see the stem more clearly, for example matrem in the accusative.

Because Latin word order is much more flexible than English word order.

A very common Latin pattern is:

• subject
• object
• verb

So Mater unam cepam et paulum allii emit is completely natural Latin word order.

Latin can do this because the endings already show the grammatical roles, so word order does not have to do as much work as it does in English.

Yes.

The sentence has two things that the mother buys, joined by et:

• unam cepam
• paulum allii

The first is a straightforward accusative noun phrase. The second is a quantity expression, where paulum is the accusative element and allii depends on it in the genitive.

So both belong with emit.