Inopia panis matrem tristem facit.

Here panis is genitive singular, not accusative. With nouns like inopia (lack, shortage), Latin often uses the genitive to show what is lacking.

So:

• inopia panis = lack of bread / shortage of bread

This is a very common Latin pattern: a noun of lacking, need, fullness, memory, and so on can take a genitive dependent on it.

Because panis is a 3rd-declension noun, and in this noun the nominative singular and genitive singular happen to look the same:

• nominative: panis
• genitive: panis

So you have to decide from the grammar of the sentence. Since inopia naturally takes a genitive, panis here is understood as genitive singular: of bread.

Because matrem is the direct object of facit.

The verb facere means to make, and in a sentence like this, it often takes:

• a person or thing being affected in the accusative
• plus a word describing what that person or thing is made to be

So:

• matrem = the mother as the person affected
• facit = makes

Because tristem agrees with matrem.

Latin often uses facio in a pattern like this:

• aliquem + adjective + facere
• to make someone + adjective

So matrem tristem facit means it makes the mother sad.

Since matrem is feminine accusative singular, the adjective describing her must match:

• matrem = feminine accusative singular
• tristem = feminine accusative singular

This is sometimes called a predicate accusative or an adjective used with a factitive verb.

Because tristis is the nominative singular form, while tristem is the accusative singular form.

Since the adjective goes with matrem, and matrem is accusative, the adjective must also be accusative:

• nominative: tristis mater = a sad mother
• accusative: matrem tristem = the mother sad / the mother as sad

So after facit, Latin uses matrem tristem, not mater tristis.

Because its subject, inopia, is singular.

Even though the sentence contains several words, only inopia is the grammatical subject. Panis depends on inopia, and matrem tristem belongs with the object side of the sentence.

So Latin sees the structure as:

• inopia panis = the lack of bread
• matrem tristem facit = makes the mother sad

Since inopia is singular, the verb is singular: facit.

It is a common Latin construction with facio:

• subject + object in the accusative + predicate adjective in the accusative + facit

In other words:

• something makes
• someone
• something/adjective

So here:

• inopia panis = subject
• matrem = direct object
• tristem = adjective describing the object after facit
• facit = makes

English does something similar: The lack of bread makes the mother sad.

Not as much as in English. Latin word order is fairly flexible because the endings show the grammatical roles.

This sentence is arranged in a very natural and clear way:

• Inopia panis first: the cause or subject
• matrem tristem next: the person affected and the result
• facit last: the verb, which is very common in Latin

A Latin author could rearrange the words for emphasis, for example:

• Matrem inopia panis tristem facit
• Tristem matrem inopia panis facit

These would still mean basically the same thing, though the emphasis would shift.

Here it means bread in a general sense.

Latin often uses the singular of a noun where English uses an uncountable idea:

• panis = bread

So inopia panis is best understood as lack of bread or bread shortage, not necessarily lack of one loaf.

Yes. In this kind of sentence, English may use several natural verbs:

• makes
• renders
• causes ... to be
• leaves

So Inopia panis matrem tristem facit could be understood as:

• The lack of bread makes the mother sad
• The shortage of bread renders the mother sad

But grammatically, Latin is still simply using facit = makes.

Because of both meaning and grammar.

First, tristem is accusative singular, which matches matrem, not inopia.
Second, the verb facit commonly takes an object plus a predicate adjective: makes the mother sad.

If tristem described inopia, it would need to agree with inopia, which is feminine nominative singular, so it would be tristis, not tristem.

So the grammar clearly shows:

• inopia = subject
• matrem = object
• tristem = description of the object