Etiam cum pluvia gravis cadat, puella in bibliotheca cum avia libenter legit.

No. They are the same Latin word, but they are doing two different jobs:

• cum pluvia gravis cadat: here cum is a conjunction, introducing a subordinate clause. In this sentence it means something like when, while, or although/even though, depending on context.
• cum avia: here cum is a preposition meaning with.

So:

• cum + verb clause = conjunction
• cum + noun in the ablative = preposition meaning with

This is very common in Latin.

Because the clause introduced by cum here is not just a plain factual when clause. With etiam and the overall sense of the sentence, it works like even though it is raining heavily or although heavy rain is falling.

Latin often uses:

• cum + subjunctive for circumstantial, causal, or concessive clauses

A concessive idea is especially likely here:

• Etiam cum pluvia gravis cadat = Even though heavy rain is falling

So cadat is present subjunctive because the cum clause is not being treated as a simple straightforward statement like when heavy rain falls.

Etiam means also, even, or still, depending on context.

Here it strengthens the cum clause and gives the sense of:

• even when
• even though

So Etiam cum pluvia gravis cadat suggests:

• Even when it is raining heavily... or
• Even though heavy rain is falling...

It adds a sense of contrast: despite the bad weather, the girl still reads happily.

Because pluvia is the subject of cadat, so it is in the nominative case.

• pluvia = nominative singular, rain
• gravis = nominative singular feminine, heavy/serious, agreeing with pluvia

So:

• pluvia gravis cadat = heavy rain falls / is falling

If it were pluviam gravem, that would be accusative, which would usually mark a direct object. But cadere (to fall) does not take a direct object here.

Because adjectives in Latin must agree with the nouns they describe in:

• gender
• number
• case

Here:

• pluvia is feminine singular nominative
• so gravis must also be feminine singular nominative

That is why you get:

• pluvia gravis = heavy rain

This is a good reminder that a 3rd-declension adjective like gravis, grave changes form to match its noun.

Because in can take two different cases with different meanings:

• in + ablative = in / inside / at a place
• in + accusative = into / onto a place, showing movement toward it

Here the girl is already in the library, not moving into it:

• in bibliotheca = in the library

If the sentence meant the girl goes into the library, then you would expect in bibliothecam.

Avia is in the ablative singular because the preposition cum meaning with takes the ablative.

So:

• cum avia = with her grandmother

This is one of the most basic uses of the ablative:

• cum + ablative = with

The main clause is:

• puella in bibliotheca cum avia libenter legit

Everything before that:

• Etiam cum pluvia gravis cadat

is a subordinate cum clause giving the circumstance or concession.

So the sentence structure is basically:

• Even though heavy rain is falling, the girl gladly reads in the library with her grandmother.

It can help to identify the main finite verb in the main clause:

• legit

Libenter means:

• gladly
• willingly
• with pleasure

It is an adverb, modifying legit.

So:

• puella ... libenter legit = the girl reads gladly

Its position is flexible. Latin word order is much freer than English word order. Here it sits near the verb it modifies, which is very natural.

Because Latin often places the verb near or at the end of the clause. This is one of the most common word-order patterns learners notice.

So:

• puella in bibliotheca cum avia libenter legit

is perfectly normal Latin word order.

That said, Latin word order is flexible, and authors can move words around for:

• emphasis
• rhythm
• style
• contrast

But a clause-final verb is extremely common.

Yes, in writing without macrons, legit can be ambiguous.

It can represent:

• legit = he/she reads (present)
• lēgit = he/she read / has read (perfect)

In fully marked Latin, the macron helps distinguish them:

• present: legit
• perfect: lēgit

In this sentence, context strongly suggests the present:

• the girl gladly reads

That fits naturally with the ongoing situation introduced by cum ... cadat.

Because Latin usually does not need an expressed subject pronoun when the verb ending already shows the person and number.

• legit = he/she/it reads

Then the noun puella makes it clear who the subject is:

• puella ... legit = the girl reads

So Latin often leaves out words like she, he, or they unless they are needed for emphasis or contrast.

Because puella is in the nominative singular, the normal case for the subject of a finite verb.

In this sentence:

• puella = nominative singular → subject
• bibliotheca = ablative after in
• avia = ablative after cum
• pluvia = nominative in the subordinate clause
• gravis = adjective agreeing with pluvia

So the sentence has:

• a subject in the subordinate clause: pluvia
• a subject in the main clause: puella

It can be understood either way in a broad sense, but here although/even though is probably the best fit.

Why?

Because:

• etiam adds a strong contrast
• the sentence seems to emphasize that despite the weather, the girl still reads happily

So the most natural understanding is:

• Even though heavy rain is falling, the girl gladly reads in the library with her grandmother.

A learner should know that cum + subjunctive often needs to be interpreted from context rather than translated mechanically with just one English word.

Yes, another order would absolutely be possible.

Latin word order is flexible because the case endings show what each word is doing. So these are all grammatically possible, for example:

• puella in bibliotheca cum avia libenter legit
• puella cum avia in bibliotheca libenter legit
• libenter puella in bibliotheca cum avia legit

The chosen order often reflects:

• what the writer wants to emphasize first
• what sounds balanced
• stylistic preference

The given order is very natural and easy:

1. subject: puella
2. place: in bibliotheca
3. companion: cum avia
4. manner: libenter
5. verb: legit

Yes. Latin can use cadere (to fall) with things like rain, just as English can say rain falls.

So:

• pluvia cadit = rain falls / is falling

This is a straightforward and idiomatic use of the verb.