In bibliotheca discipulus sedens litteras poetae veteris describit.

Because in with a place where something happens normally takes the ablative in Latin.

So:

• in bibliotheca = in the library

If in showed motion into somewhere, it would usually take the accusative instead:

• in bibliothecam = into the library

This is a very common distinction in Latin:

• in + ablative = location
• in + accusative = motion toward

Discipulus is nominative singular. It is the subject of the sentence.

That means discipulus is the one doing the action of describit.

You can see this from both meaning and form:

• discipulus = nominative singular, the student
• describit = he/she/it copies, writes out, describes

So discipulus is the person who is copying.

Sedens is the present active participle of sedeo, meaning sitting.

Here it agrees with discipulus and describes the student:

• discipulus sedens = the sitting student or the student sitting

A participle is a verbal adjective, so it has both:

• a verbal sense: sitting
• an adjectival sense: it describes a noun

Latin often uses participles where English might use:

• a relative clause: the student who is sitting
• or a simpler adjective-like phrase: the sitting student

Not exactly.

• sedet = he/she is sitting
• sedens = sitting

So:

• discipulus sedet = the student is sitting
• discipulus sedens describit = the student, sitting, copies...

In your sentence, sedens is not the main verb. The main verb is describit.
Sedens adds extra information about the subject.

Litteras is accusative plural, because it is the direct object of describit.

It answers the question what is the student copying?

• discipulus ... describit litteras = the student copies the letters / writings

As for the plural, litterae in Latin often appears in the plural with meanings such as:

• letters of the alphabet
• a letter / epistle
• literature / learning / writings, depending on context

So the plural here is not strange in Latin. It is simply the normal dictionary form for several common meanings.

Because it shows possession or association: of an old poet.

• poetae = genitive singular of poeta
• veteris = genitive singular of vetus

Together they modify litteras:

• litteras poetae veteris = the letters/writings of an old poet

The genitive is often the Latin case for of ....

Because some Latin nouns referring to male people belong to the first declension even though first-declension nouns are often feminine.

Poeta is one of those common exceptions:

• poeta, poetae = poet
• grammatically masculine

Other similar nouns include:

• agricola = farmer
• nauta = sailor
• incola = inhabitant

So poetae veteris is perfectly normal:

• poetae = genitive singular
• masculine in meaning, first declension in form

We know from case, number, and gender agreement.

• litteras is accusative plural feminine
• poetae here is genitive singular
• veteris is genitive singular

Since veteris is genitive singular, it matches poetae, not litteras.

So:

• poetae veteris = of an old poet

If Latin wanted old letters, the adjective would have to agree with litteras, so the form would be different.

In this context, describit most naturally means copies out, transcribes, or writes down.

Although a beginner may connect it with English describe, Latin describere often has the sense of:

• copying from a model
• writing out
• transcribing

So in a library context, describit probably suggests that the student is copying the writings of an old poet, not merely giving a verbal description of them.

This is a good example of a word that looks familiar in English but does not always mean exactly the same thing.

Latin word order is much more flexible than English word order because Latin shows grammatical function mainly through endings, not position.

So Latin can place words in an order that highlights:

• emphasis
• style
• rhythm
• what belongs together in sense

In this sentence:

• In bibliotheca comes first to set the scene
• discipulus sedens stays together as a noun phrase
• litteras poetae veteris stays together as the object phrase
• describit comes at the end, which is very common in Latin

English depends much more on order:

• subject before verb
• object after verb

Latin does not depend on that nearly as much.

Yes, Latin could move sedens to another position, as long as the meaning remained clear.

For example, Latin often allows a lot of rearrangement for style or emphasis. But keeping sedens near discipulus is the clearest and most natural arrangement, because sedens modifies discipulus.

So in your sentence, discipulus sedens is a neat, easy-to-read phrase:

• the student sitting

Because Classical Latin has no definite article and no indefinite article.

So:

• discipulus can mean the student or a student
• bibliotheca can mean the library or a library
• poetae veteris can mean of the old poet or of an old poet

English must choose between a/an and the, but Latin usually leaves that to context.

No. Sedens does not need a separate is in Latin when it is used as a participle modifying a noun.

So:

• discipulus sedens = the student sitting
• not the student is sitting as a complete statement by itself

If Latin wanted to make is sitting the main idea, it would use a finite verb such as sedet.

In this sentence, the main action is describit, and sedens is just additional description of the student.