Puer celeriter ad scholam currit, sed puella tarda domi manet et statim dormit.

Because ad takes the accusative case when it means to/toward a place.

• schola = the basic dictionary form, nominative singular
• ad scholam = to the school

So Puer ... ad scholam currit means The boy runs to school.

Ad + accusative commonly expresses movement toward a place: to, toward.

So:

• ad scholam = to the school / to school

Latin can also use in + accusative for motion into something, but ad is a very natural choice here for going to school. A learner should understand ad scholam as a normal way to say this.

Both are in the nominative case because they are the subjects of their verbs.

• puer ... currit = the boy runs
• puella ... manet ... dormit = the girl stays ... sleeps

In Latin, the nominative is typically used for the doer of the action.

They do different jobs.

• celeriter modifies the verb currit: it tells how the boy runs.
  
  • celeriter = quickly
• tarda modifies puella: it describes what kind of girl she is.
  
  • puella tarda = the slow/sluggish girl

A native English speaker may expect something like slowly in the second clause, but Latin here says the slow girl stays at home, not the girl stays home slowly.

Because tarda must agree with puella.

• puella is feminine singular nominative
• so the adjective must also be feminine singular nominative
• therefore: tarda

If the noun were puer, you would expect tardus.

Domi means at home. It is a special form called the locative.

A few place words in Latin have special forms for location, and domus is one of them:

• domi = at home
• domum = homeward / to home
• domo = from home

So domi manet means she stays at home.

They are all present tense, third person singular, active voice.

• currit = he/she runs
• manet = he/she remains / stays
• dormit = he/she sleeps

Because the subjects are explicitly given:

• puer currit = the boy runs
• puella manet = the girl stays
• puella dormit = the girl sleeps

In Latin, the verb ending already tells you the person and number.

For example:

• currit = he/she/it runs
• manet = he/she/it stays
• dormit = he/she/it sleeps

Latin does not need to add he or she unless it wants emphasis or clarity. In this sentence, the nouns puer and puella make the subjects completely clear.

Latin word order is more flexible than English because the endings show grammatical function.

English relies heavily on position:

• The boy runs to school

Latin can move words around more freely:

• Puer celeriter ad scholam currit
• Celeriter puer ad scholam currit
• Ad scholam puer celeriter currit

These can all mean roughly the same thing, though the emphasis may shift. In the given sentence, the order is natural and easy to follow.

They are conjunctions.

• sed = but
• et = and

So the sentence has this structure:

• Puer celeriter ad scholam currit
  but
• puella tarda domi manet
  and
• statim dormit

This gives a contrast between the boy and the girl, and then adds a second action for the girl.

Statim is an adverb meaning immediately / at once. It modifies dormit.

So:

• statim dormit = she immediately sleeps / she goes to sleep at once

It tells you when/how promptly the sleeping happens.

It can suggest slow, sluggish, unhurried, or sometimes lazy, depending on context.

In this sentence, since the meaning is already known to the learner, the key grammar point is that tarda is simply describing puella. It is not an adverb. So the idea is something like:

• the slow/sluggish girl stays at home

The exact nuance depends on context.

Classical Latin has no articles like English the and a/an.

So:

• puer can mean the boy or a boy
• puella can mean the girl or a girl
• scholam can mean the school or just school, depending on context

English has to choose an article, but Latin usually leaves that to context.

Yes, that is possible as a nuance. The adjective tarda agrees with puella, so it can be felt as either:

• the slow girl stays at home
  or
• the girl, slow as she is, stays at home

In a simple learner sentence, the first interpretation is usually the easiest. But Latin adjectives can sometimes feel slightly more flexible than their most literal English translation.

Because one subject can govern more than one verb.

Here, puella is the subject of both:

• manet = stays
• dormit = sleeps

Latin does not need to repeat the noun:

• puella tarda domi manet et statim dormit
  = the slow girl stays at home and immediately sleeps

This is completely normal in both Latin and English.