Salix prope rivum stat, et puella sub salice sedet.

Because the same noun is being used in two different cases.

• salix = nominative singular, used for the subject: the willow is doing the action.
• salice = ablative singular, used after sub here because the girl is sitting under the willow.

This noun belongs to the third declension:

• nominative: salix
• genitive: salicis
• stem: salic-

So the change from salix to salice is normal Latin inflection.

Because prope takes the accusative case.

So:

• prope rivum = near the stream

Even though in English we just say near the stream, Latin requires the noun after prope to be in the accusative.

• rivus = nominative
• rivum = accusative

This is something you simply learn with the preposition: prope + accusative.

With sub, Latin often uses:

• ablative for location/rest: under
• accusative for motion toward: to under / underneath

Here the girl is already sitting there, so there is no movement. That is why Latin uses the ablative:

• sub salice = under the willow

If someone were moving to a position under the tree, Latin could use the accusative instead.

Both are third person singular present tense verbs.

• stat = stands / is standing
• sedet = sits / is sitting

They each end in -t, which often marks he/she/it in the present tense.

So:

• salix ... stat = the willow stands
• puella ... sedet = the girl sits

Latin usually does not need a separate subject pronoun like she or it, because the verb ending already tells you the person and number.

Classical Latin has no articles.

So:

• salix can mean a willow or the willow
• puella can mean a girl or the girl
• rivum can mean a stream or the stream

You decide from the context which English article makes the most sense.

Mostly from the case endings and the verb forms, not from word order alone.

• salix is nominative, so it is the subject of stat
• puella is nominative, so it is the subject of sedet
• rivum is accusative because it goes with prope
• salice is ablative because it goes with sub in a place/location sense

Latin is much more dependent on endings than English is.

Yes, but not in the same way as in English.

The basic meaning does not depend entirely on word order, because the endings show the grammatical roles. Latin could rearrange the sentence in different ways and still mean the same thing.

For example, the idea of the sentence would still be clear even if the words were moved around, because:

• salix and puella are clearly subjects
• rivum and salice are marked by their cases

However, the given order is natural and easy:

• Salix prope rivum stat
• et puella sub salice sedet

It presents each subject and then its location and action in a straightforward way.

They are not all from the same declension.

• salix, salicis = third declension, feminine
• rivus, rivi = second declension, masculine
• puella, puellae = first declension, feminine

That is why their forms change differently:

• rivus → rivum
• salix → salice

Learning declensions helps you predict these changes.

Salix is grammatically feminine. In Latin, grammatical gender is part of the noun, and it does not always work the same way as natural gender in English.

A useful pattern is that many tree names in Latin are feminine, and salix follows that pattern.

So if you later see an adjective agreeing with salix, it would normally be feminine as well.

In Latin, stare can be used quite naturally for something that is standing upright or positioned somewhere. So a tree stands near a stream is a normal Latin way to express that the tree is there in an upright position.

Similarly:

• sedere = to sit
• stare = to stand

Latin often likes these concrete physical verbs.

Et means and. It joins the two parts of the sentence:

• Salix prope rivum stat
• puella sub salice sedet

So the whole sentence gives two connected facts:

• the willow stands near the stream
• and the girl sits under the willow

Sometimes Latin can connect ideas without et, especially in certain styles, but in a simple sentence like this, et is the normal and clear way to say and.

So here it straightforwardly links the two clauses.

They can often cover both ideas, depending on context.

So:

• stat can mean stands or is standing
• sedet can mean sits or is sitting

Latin does not make this distinction in the same obligatory way English does. The context tells you which English translation sounds best.