Na estante da biblioteca, encontrei um livro com observações importantes na primeira página.

Because na is a contraction of em + a.

• na estante = on/in the bookshelf
• na primeira página = on the first page

In Portuguese, em often combines with the definite article:

• em + a = na
• em + o = no
• em + as = nas
• em + os = nos

So instead of saying em a estante, Portuguese normally says na estante.

For the same reason: Portuguese commonly contracts de with definite articles.

• de + a = da
• de + o = do
• de + as = das
• de + os = dos

So:

• a estante da biblioteca = the bookshelf of the library / the library bookshelf

This is extremely common in Portuguese.

Portuguese allows flexible word order, especially when you want to set the scene first.

So:

• Na estante da biblioteca, encontrei um livro... = On the library bookshelf, I found a book...

Starting with the location gives a natural setting-first feel. It is similar to English sentences like:

• On the table, I found my keys.

You could also say:

• Encontrei um livro na estante da biblioteca...

That version is also correct and very natural.

Encontrei is the first-person singular form of the pretérito perfeito of encontrar.

• encontrar = to find
• encontrei = I found

This tense is used for a completed action in the past.

Examples:

• Encontrei um livro. = I found a book.
• Comprei um café. = I bought a coffee.
• Cheguei cedo. = I arrived early.

Um livro means a book, so it introduces the book as something not previously identified.

• um livro = a book
• o livro = the book

If you say um livro, the listener does not yet know which book.
If you say o livro, you are talking about a specific book already known from context.

So here, um livro is natural because the book is being introduced for the first time.

It describes um livro.

So the phrase means:

• a book with important notes/observations

Structure:

• um livro
• com observações importantes

This is similar to English a book with important notes.

Here, com means with, and it links the book to what it contains.

Because it agrees with observações, which is feminine plural.

• observação = singular
• observações = plural
• importante = singular form
• importantes = plural form

So:

• observação importante = important observation/note
• observações importantes = important observations/notes

In Portuguese, adjectives usually agree in number and often gender with the noun they describe.

Because it agrees with página, which is a feminine noun.

• página = feminine singular
• primeiro = masculine singular
• primeira = feminine singular

So:

• o primeiro capítulo = the first chapter
• a primeira página = the first page

Ordinal numbers like primeiro/primeira must agree with the noun.

In context, it most naturally tells you where the observations were: on the first page.

So the sentence is usually understood as:

• I found a book
• and that book had important observations
• on the first page

However, structurally, Portuguese can sometimes allow a little ambiguity, just like English can. If you wanted to make it clearer, you could say:

• Na estante da biblioteca, encontrei um livro que tinha observações importantes na primeira página.

That makes the relationship more explicit.

• estante = bookshelf or bookcase
• biblioteca = library

So a estante da biblioteca means the bookshelf in the library or the library’s bookshelf.

A learner might confuse biblioteca with bookstore, but in Portuguese:

• biblioteca = library
• livraria = bookstore

That is a very common vocabulary point for English speakers.

Yes, it is grammatically possible, but it sounds a little less clear because the final na estante da biblioteca may momentarily seem to attach to página.

Portuguese often places the location earlier to avoid confusion:

• Na estante da biblioteca, encontrei um livro...

or

• Encontrei, na estante da biblioteca, um livro...

Both help the reader understand right away that on the bookshelf in the library is the place where the book was found.

Not necessarily. In this sentence, observações could mean several things depending on context, such as:

• notes
• remarks
• comments
• observations

If this is about writing inside a book, English often prefers notes.
So even if the dictionary says observações = observations, the most natural translation in context may be notes.

That is a good example of how Portuguese vocabulary often depends on context, not just direct word-for-word matching.