Donec pluvia desinat, mulier iuxta rivum sub arbore manere vult.

Desinat is present subjunctive, and that is very common after donec when the action is still anticipated rather than presented as a simple fact already reached. In other words, the stopping of the rain is something looked forward to.

So:

• donec pluvia desinat = until the rain stops
• more literally, with the nuance: until the rain should stop

An English speaker usually just translates it naturally, but the Latin mood choice is important.

Pluvia is nominative singular. It is the subject of desinat, because the rain is the thing that is doing the stopping.

So the structure is:

• pluvia = subject
• desinat = verb

Even though English says the rain stops, Latin works the same way here: rain is the subject.

Because Latin gender does not depend only on the ending. While many first-declension nouns in -a are feminine, plenty of feminine nouns belong to other declensions too.

Mulier is a third-declension feminine noun, and it means woman. So you simply have to learn its gender as part of the vocabulary entry.

Because it depends on vult. Latin often uses a complementary infinitive after verbs like:

• vult = wants
• potest = is able
• debet = ought

So:

• vult manere = wants to remain

This is very similar to English wants to stay/remain, where to remain is also an infinitive.

Because its subject is mulier, which is singular. The verb has to agree with its subject in number and person.

So:

• mulier vult = the woman wants
• if it were plural, it would be mulieres volunt = the women want

Because iuxta is a preposition that regularly takes the accusative case.

So:

• iuxta rivum = beside the stream

Here rivum is the accusative singular of rivus.

This is something you learn with the preposition itself: iuxta + accusative.

With sub, the case depends on the meaning:

• sub + ablative = location: under something
• sub + accusative = motion toward a position under something

Here the idea is remaining in a place, not moving into it, so Latin uses the ablative:

• sub arbore = under the tree

If the sentence were about moving to a place under the tree, Latin could use sub arborem instead.

Yes. Both prepositional phrases give location, and both go naturally with manere.

So the sense is that she wants to remain:

• iuxta rivum = beside the stream
• sub arbore = under the tree

They do not conflict; they simply give a more detailed picture of where she is.

Because Classical Latin has no articles like English the and a/an. Latin often leaves that idea to context.

So:

• mulier can mean a woman or the woman
• rivum can mean a stream or the stream
• arbore can mean a tree or the tree

The translator chooses the most natural English wording from the context.

Yes. Latin word order is much freer than English word order because the endings show the grammatical relationships.

This sentence puts the time clause first:

• Donec pluvia desinat, then the main clause

And in the main clause, the verb vult comes at the end, which is very natural in Latin:

• mulier iuxta rivum sub arbore manere vult

But other arrangements are possible, for example:

• Mulier sub arbore iuxta rivum manere vult, donec pluvia desinat.

That would still be grammatical. The original order simply has a natural flow and emphasis.