Si pluvia non caderet, mulier iuxta rivum maneret.

Because this sentence is expressing a hypothetical, unreal situation, not a simple statement of fact.

In Latin, a condition like if X were happening, Y would happen is often called a present contrary-to-fact condition. Latin regularly uses the imperfect subjunctive in both clauses for that pattern:

• Si pluvia non caderet = if the rain were not falling
• mulier iuxta rivum maneret = the woman would remain beside the stream

So the subjunctive here signals that the speaker is imagining a situation that is not actually true.

This is a present contrary-to-fact conditional.

That means:

• the if-clause describes something unreal in the present
• the main clause describes what would happen if that unreal condition were true

Pattern:

• si
  • imperfect subjunctive
• main clause + imperfect subjunctive

So this sentence means something like:

• If it were not raining, the woman would stay beside the stream

The implication is that it is in fact raining, so she is not staying there.

That is a very common point of confusion for English speakers.

In this construction, the imperfect subjunctive does not mainly indicate past time. Instead, it marks an unreal present situation.

So:

• caderet does not mean simply was falling
• maneret does not mean simply was remaining

In this kind of sentence, they mean:

• were falling / were not falling
• would remain

English also does something similar when it says If it were raining... Even though were looks past, it often expresses an unreal present situation.

Caderet comes from the verb cadere, meaning to fall.

It is the 3rd person singular imperfect subjunctive active.

How it is built:

• infinitive: cadere
• add the personal ending for he/she/it: -t
• result: caderet

This is the normal way to form the imperfect subjunctive in Latin:

• amare → amaret
• monere → moneret
• regere → regeret
• audire → audiret
• cadere → caderet

Since the subject is pluvia (rain), the singular verb form makes sense.

Maneret comes from manere, meaning to remain, stay, or wait depending on context.

It is also 3rd person singular imperfect subjunctive active.

Formation:

• infinitive: manere
• add -t
• result: maneret

Because the subject is mulier (the woman), the verb is singular.

Non normally goes directly before the word it negates, and here it negates the verb caderet.

So:

• pluvia non caderet = the rain were not falling

This is the most straightforward and common placement.

Latin word order is flexible, but non is very often placed immediately before the verb or other word being negated.

Both pluvia and mulier are in the nominative singular because each is the subject of its clause.

• pluvia = subject of caderet
• mulier = subject of maneret

So the structure is:

• Si pluvia non caderet
  pluvia = the thing doing the falling

• mulier iuxta rivum maneret
  mulier = the person doing the remaining

Good question. Rivum is accusative because it is the object of the preposition iuxta.

Iuxta means next to, beside, or near, and it takes the accusative case.

So:

• iuxta rivum = beside the stream

Even though the phrase expresses location in English, Latin does not always use the ablative for location. It depends on the preposition.

Examples:

• in villa = in the house → in
  • ablative for location
• ad villam = to the house → ad
  • accusative
• iuxta rivum = beside the stream → iuxta
  • accusative

So the accusative here is required by iuxta.

Here iuxta is a preposition meaning:

• beside
• next to
• near

So iuxta rivum means beside the stream or next to the stream.

In some contexts, iuxta can also have the sense according to, especially in later or less common usage, but that is not the meaning here.

Yes, Latin can use pluvia cadit literally rain falls to express it is raining.

So:

• pluvia cadit = it is raining
• pluvia non caderet = the rain were not falling / it were not raining

This is more concrete than English it is raining, but it is perfectly natural Latin.

Because Latin usually expresses that idea through the subjunctive verb form itself, rather than by adding a separate word like English would.

So:

• maneret by itself can mean would remain in this kind of conditional sentence

Latin has no single direct equivalent of English auxiliary would that works the same way in all contexts. Instead, Latin uses verb mood and tense to show the meaning.

That is why both clauses are in the imperfect subjunctive, and English translates the result clause with would.

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

For example, the sentence could be rearranged without changing the basic meaning:

• Si non pluvia caderet, mulier iuxta rivum maneret
• Mulier si pluvia non caderet iuxta rivum maneret
• Iuxta rivum mulier maneret, si pluvia non caderet

However, some orders sound more natural than others. The given version is clear and straightforward:

• condition first
• result second

That is a very common arrangement in Latin.

Yes: that is a very common Latin style.

Latin often places the verb:

• at the end of the clause
• or near the end

So in this sentence:

• Si pluvia non caderet
• mulier iuxta rivum maneret

both verbs come last, which gives the sentence a very natural Latin rhythm.

It is not an absolute rule, but it is extremely common and something learners should get used to seeing.