Learn Hardcore Latin: Cras magister ad scholam nuntium mittet et cum discipulis novam amicitiam faciet. - Tomorrow the teacher will send a message to the school and will make a new friendship with the students.

Magister is nominative singular (masculine).
It is the subject of both verbs mittet (will send) and faciet (will make).
So: magister = the teacher (he) will send … and (he) will make ….

What is cras, and why does it come at the start of the sentence?

Cras is an adverb meaning tomorrow.
Latin adverbs do not change their form for case, number, or gender.

It can appear in several positions in a sentence, but putting cras at the beginning is a normal way to mark the time frame of the whole statement: Tomorrow, the teacher will…

What does ad scholam mean exactly, and what case is scholam?

Ad scholam literally means to the school or toward the school.

Ad normally takes the accusative case and expresses direction or motion toward something.
Scholam is accusative singular, from schola, -ae (a first-declension feminine noun).

So ad scholam = to the school as the destination of mittet (will send).

What exactly is nuntium here: a messenger or a message, and what form is it?

Nuntium is accusative singular masculine, from nuntius, -i.
Grammatically it is the direct object of mittet: the teacher will send a nuntius.

The word nuntius / nuntium can mean:

a messenger (person)
a message (thing)

In many school-style sentences, it is often taken as “messenger”, so: He will send a messenger to the school.
Context in a longer passage would decide whether messenger or message fits better.

How do we know that mittet is future tense, and what is its basic dictionary form?

Mittet ends in -et, which here marks 3rd person singular future active indicative in the 3rd conjugation.

Dictionary form: mitto, mittere, misi, missum (to send).
Future indicative singular: mittam, mittes, mittet, mittemus, mittetis, mittent.

So mittet = he / she / it will send (here: the teacher will send).
No separate word like will is needed in Latin; the ending shows the tense.

Where is the English word “will” in this sentence? How does Latin show the future in mittet and faciet?

Latin does not use a separate word like will to form the future.
Instead, the verb ending itself marks the future tense.

mittet: mitto in the future, 3rd person singular → he will send
faciet: facio in the future, 3rd person singular → he will make

So the idea of will is built into -et in both mittet and faciet.

Why is magister not repeated before faciet? How do we know the subject of faciet?

Latin usually does not repeat the subject if it stays the same.

We have:

magister … nuntium mittet
et … novam amicitiam faciet

Because no new subject is introduced, we understand that magister is still the subject of faciet.
So the sense is: The teacher will send … and (the teacher) will make ….

What case is discipulis, and why is it discipulis instead of discipulos?

Discipulis is ablative plural (masculine), from discipulus, -i (student, pupil).
It is governed by cum, which normally takes the ablative to express accompaniment (with).

cum discipulis = with the students (ablative of accompaniment)
discipulos would be accusative plural and would normally be a direct object, which is not the role here.

So cum discipulis correctly means together with the students.

What does cum discipulis do in the sentence?

Cum discipulis is an ablative phrase of accompaniment.

It tells us with whom the teacher will make the new friendship:

cum = with
discipulis = the students (ablative plural)

So faciet is not just he will make a new friendship, but he will make a new friendship with the students.

Why is it novam amicitiam and what case is it in?

Novam amicitiam is in the accusative singular (feminine):

amicitiam = accusative singular of amicitia, -ae (friendship)
novam = accusative singular feminine of novus, -a, -um (new), agreeing with amicitiam

Novam amicitiam is the direct object of faciet: he will make a new friendship.

Is amicitiam facere just literally “to make a friendship,” or is it an idiom?

Amicitiam facere (cum aliquo) is a standard Latin expression meaning:

to make a friendship (with someone)
more naturally in English: to form / establish / enter into a friendship.

So cum discipulis novam amicitiam faciet can be understood as:

he will form a new friendship with the students, not that he is literally manufacturing a physical object.

Can the word order of this sentence be changed without changing the basic meaning?

Yes. Latin word order is much freer than English because the endings show the roles of words.

For example, all of these keep the same core meaning:

Magister cras nuntium ad scholam mittet et cum discipulis novam amicitiam faciet.
Cras nuntium magister ad scholam mittet et novam amicitiam cum discipulis faciet.

These changes might slightly shift emphasis, but the grammatical relationships (who does what to whom) stay clear from the endings (cases and verb forms).

Do mittet and faciet happen at the same time, or one after the other?

The simple future in Latin just says they will both happen in the future.
By itself, it does not specify whether:

he will first send the messenger and then make the friendship,
or whether these actions are roughly contemporaneous.

Often the context or common sense tells us the likely order. In a typical narrative, English tends to understand it as sequence: he will send … and (after that) he will make …, but Latin does not grammatically force that sequence here.