In bibliotheca hic codex lente legendus est, quia scriptura eius difficilis est.

Because in takes different cases depending on the meaning:

• in + ablative = location, in / inside
• in + accusative = motion toward, into

So in bibliotheca means in the library.
If the sentence meant into the library, it would be in bibliothecam.

Hic means this. It is a demonstrative adjective modifying codex.

It is hic because it must agree with codex in:

• gender: masculine
• number: singular
• case: nominative

So:

• masculine nominative singular: hic
• feminine nominative singular: haec
• neuter nominative singular: hoc

Since codex is masculine singular nominative, hic is the correct form.

Because codex is a third-declension noun, not a second-declension noun.

Its nominative singular is codex, and that form can perfectly well be the subject of the sentence. Latin subjects are not identified by a special word order or by ending in -us; they are identified by their case and their grammatical role.

Here hic codex is nominative singular, so it is the subject: this codex.

This is the passive periphrastic, a very important Latin construction.

It is made of:

• a gerundive: legendus = to be read
• a form of esse: est = is

Together, they express necessity, obligation, or something that ought to be done.

So codex legendus est means:

• the codex must be read
• the codex ought to be read
• literally, the codex is to-be-read

Because codex is masculine singular, the gerundive also appears as masculine singular: legendus.

Latin does not have to state the agent in this construction.

So hic codex lente legendus est can mean, in a general way:

• this codex must be read slowly
• one should read this codex slowly

If Latin wanted to specify who has the obligation, it could use the dative of agent:

• nobis hic codex lente legendus est = we must read this codex slowly
• tibi hic codex lente legendus est = you must read this codex slowly

Since no agent is given here, the obligation is left general.

Lente is the adverb meaning slowly.

It comes from the adjective lentus, -a, -um, meaning slow or calm.
In this sentence, we need an adverb because it modifies the verbal idea legendus est:

• not a slow codex
• but read slowly

So:

• lentus codex = a slow codex or a sluggish codex if that made sense
• lente legendus est = must be read slowly

In context, it can suggest both.

The basic meaning is slowly, but when someone reads something slowly because it is hard, the idea often becomes:

• slowly
• with care
• carefully

So the Latin is straightforwardly slowly, but the context naturally adds the sense of careful reading.

This is a very common and important question.

• suus, sua, suum is a reflexive possessive: it refers back to the subject of its own clause
• eius means his / her / its, referring to someone or something else

In the clause quia scriptura eius difficilis est, the subject is scriptura.
The possessor is the codex from the main clause.

Since the possessor is not the subject of this subordinate clause, Latin uses eius, not sua.

So:

• scriptura eius = its writing
• scriptura sua would suggest its own writing, referring back to scriptura itself, which is not what is meant here

Here scriptura means something like:

• writing
• script
• handwriting
• the written style or lettering

So scriptura eius difficilis est means that the codex is hard to read because its writing is difficult—perhaps because the handwriting, script style, or letter forms are hard to make out.

It does not mean the content is difficult so much as the written form is difficult.

Because it agrees with scriptura.

Scriptura is:

• feminine
• singular
• nominative

So the adjective must match it:

• scriptura difficilis = the writing is difficult

Even though difficilis looks the same for masculine and feminine in the nominative singular, it is still agreeing correctly with the feminine noun scriptura.

Yes, Latin word order is much freer than English word order because the endings carry so much grammatical information.

This sentence puts emphasis roughly like this:

• In bibliotheca first: setting or location
• hic codex next: the thing being discussed
• lente legendus est: what must be done
• quia...: the reason

A rearranged version could still mean the same thing, for example:

• Hic codex in bibliotheca lente legendus est, quia scriptura eius difficilis est.
• Quia scriptura eius difficilis est, hic codex in bibliotheca lente legendus est.

The original order is natural and clear, but Latin is not tied to one rigid pattern like English is.

Because there are really two clauses, and each has its own verbal idea:

1. hic codex lente legendus est
   = this codex must be read slowly

2. quia scriptura eius difficilis est
   = because its writing is difficult

In both clauses, est is the verb is.

• In the first clause, it combines with the gerundive legendus.
• In the second clause, it links scriptura with difficilis.

So the two est forms are doing different jobs in two different clauses.