Puer paulisper in limine sedet, deinde ad matrem currit.

Puer is the subject of both verbs, sedet and currit, so it is in the nominative case.

• puer = the boy as subject
• puerum = the boy as direct object

Since the boy is the one doing the actions, Latin uses puer.

Paulisper is an adverb, and it means for a little while or briefly.

It modifies the verb sedet, telling us how long the boy sits:

• Puer paulisper in limine sedet = The boy sits on the threshold for a little while

It does not change form, because adverbs in Latin are indeclinable.

After in, Latin can use different cases depending on the meaning.

Here, in limine uses the ablative case because in means in/on/at a place, expressing location rather than motion.

• in + ablative = location
• in + accusative = motion into/onto

So:

• in limine = on the threshold / at the doorway
• If it meant into the threshold or onto the threshold in a motion sense, Latin would use a different construction.

Limine is the ablative singular of limen.

Limine is ablative singular.

Its dictionary form is:

• limen, liminis = threshold, doorway

This is a third-declension neuter noun. Some important forms are:

• nominative singular: limen
• genitive singular: liminis
• ablative singular: limine

So in this sentence, in limine means on the threshold or at the doorway.

The verb curro often uses ad + accusative to show motion toward someone or something.

So:

• ad matrem = to/toward his mother

Without ad, matrem by itself would look like a direct object, which would be confusing, since currere does not normally take a direct object in this meaning.

This is a very common Latin pattern:

• ad villam venit = he comes to the house
• ad amicum currit = he runs to his friend

Matrem is accusative singular of mater, matris.

It is accusative because it follows the preposition ad, and ad takes the accusative case.

So:

• mater = mother as subject
• matrem = mother after ad, meaning to the mother

Both sedet and currit are present tense, third person singular.

• sedet = he/she sits or is sitting
• currit = he/she runs or is running

Because the subject is puer, both verbs mean:

• the boy sits
• the boy runs

Latin present tense can often be translated in more than one natural English way:

• sits
• is sitting depending on context.

In Latin, one subject can easily go with more than one verb if the meaning is clear.

Here, puer is the subject of both:

• sedet
• currit

So the sentence means:

• The boy sits for a little while on the threshold, then runs to his mother.

Latin does not need to repeat puer before the second verb unless the writer wants extra emphasis or clarity.

Deinde is an adverb meaning then, next, or afterward.

It connects the two actions in sequence:

1. Puer paulisper in limine sedet
2. deinde ad matrem currit

So it shows that the boy first sits for a little while, and after that he runs to his mother.

Yes. Latin word order is flexible because the endings show the grammatical relationships.

This sentence is quite straightforward and natural:

• Puer paulisper in limine sedet, deinde ad matrem currit.

But Latin could rearrange it in other ways without changing the basic meaning, for example:

• Paulisper puer in limine sedet
• Ad matrem deinde currit puer

The differences would usually be about emphasis, not core meaning.
In the original sentence, the order is easy and narrative:

• subject first
• then details
• then verb
• then deinde introducing the next action

By themselves, sedet and currit just mean he/she/it sits and he/she/it runs, because Latin third-person singular verb forms do not show gender.

You know the subject is he here because of puer, which means boy.

So:

• puer ... sedet = the boy sits
• puer ... currit = the boy runs

If the subject were feminine, the verb forms could stay exactly the same:

• puella sedet = the girl sits

Latin often leaves out possessive words like his when the relationship is obvious from context.

Here, ad matrem literally means to the mother, but in natural English it is usually understood as to his mother because the subject is a boy and the context makes the relationship clear.

Latin frequently does this with family members:

• patrem vocat = he calls his father
• ad matrem venit = he comes to his mother

If Latin wanted to be especially explicit, it could say ad matrem suam, but that is not necessary here.