Hún skilar bókinni í bókasafnið á morgun.

Hún is the Icelandic subject pronoun for she. Icelandic has different forms of pronouns depending on grammatical case (nominative, accusative, dative, genitive). Here it’s the subject of the sentence, so it’s in the nominative: hún.

Skilar is the present tense, 3rd person singular form of the verb skila (to return / to hand in / to deliver back).
So: ég skila (I return), þú skilar (you return), hún skilar (she returns).

Bókinni is the book in the dative singular. The verb skila commonly takes what you return as a dative object.

• bók = a book (basic form)
• bókin = the book (nominative)
• bókinni = (to/with) the book (dative; used here as the object with skila)

The -ni is part of the dative definite form.

Yes—skila is typically treated as a dative-taking verb for the thing being returned/handed in. Learners often remember it as:
skila + dative (the item), and often also a destination with a preposition (like í).

Because í can govern different cases depending on meaning:

• í + accusative = motion into (destination)
• í + dative = location in (being there)

Here she is returning it to/into the library (a destination), so it’s accusative: bókasafnið (the library, accusative singular).

Bókasafn means a library (indefinite).
Bókasafnið means the library (definite).

Icelandic usually marks the by attaching a suffix (here -ið) rather than using a separate word.

Á morgun is the standard idiomatic way to say tomorrow (literally something like on tomorrow). It’s just the normal Icelandic expression; you typically don’t translate the preposition word-for-word.

They’re flexible, but a very common neutral order is: Subject + verb + objects + place + time, which matches this sentence well.
You can also front time for emphasis: Á morgun skilar hún bókinni í bókasafnið.
That’s still correct and common.

Usually no in standard Icelandic. Icelandic normally requires an explicit subject (unlike Spanish/Italian). You’d typically keep hún, unless the subject is expressed in some other way in context (or in special styles like notes/commands).

Add ekki (not), typically after the verb phrase: Hún skilar bókinni ekki í bókasafnið á morgun.
Depending on what you’re negating/emphasizing, ekki can move:

• Hún skilar ekki bókinni í bókasafnið á morgun. (she won’t return the book)

The past tense of skila is skilaði: Hún skilaði bókinni í bókasafnið. (She returned the book to the library.)
For tomorrow, you’d obviously change the time phrase (e.g., í gær = yesterday) if needed: Hún skilaði bókinni í bókasafnið í gær.