Learn Italian: Il settimo e l'ottavo libro sono nuovi. - The seventh and eighth books are new.

In Italian, when you use ordinal numbers with separate articles to talk about individual items (literally "the seventh and the eighth book"), the noun usually stays singular. English often groups them into the plural "books", but Italian treats them as distinct single items within the phrase.

If libro is singular, why do we use the plural verb sono and the plural adjective nuovi?

Even though the word libro is singular, you are talking about two books in total! The complete subject is "the seventh book and the eighth book". Since there is more than one book overall, the verb must be the plural sono (are) and the adjective must be the plural nuovi (new).

Why does ottavo have l' in front of it instead of il?

Ottavo (eighth) starts with a vowel. Because it acts as an adjective before the masculine noun libro, it takes the masculine article lo. As a quick reminder from earlier lessons, whenever lo is placed before a vowel, it drops its "o" and becomes l'.

Do ordinal numbers like settimo always end in "-o"?