Вдобавок она посоветовала мне сборник рассказов, о котором я раньше даже не слышала.

Вдобавок means in addition, besides, or on top of that. It connects this sentence to something mentioned before and adds one more thing she did.

It is similar to к тому же or кроме того, though вдобавок can sound a bit more like as an extra.

This is an aspect question.

• посоветовала is perfective
• советовала is imperfective

Here, посоветовала shows a completed single act: she gave that recommendation.
If you used советовала, it could suggest a repeated action, an ongoing process, or simply describe the recommendation less as a completed event.

Also, the ending -ла shows the subject is feminine: она посоветовала.

Because советовать / посоветовать usually follows the pattern:

посоветовать кому? что?
= to recommend/advice someone something

So:

• мне = dative, the person receiving the recommendation
• сборник рассказов = the thing being recommended

So the structure is: она посоветовала мне сборник рассказов = she recommended a collection of stories to me.

Сборник means collection, compilation, or anthology.
Рассказов is the genitive plural of рассказ, which usually means a short story in a literary sense.

So сборник рассказов is not just a bunch of stories in a casual sense. It usually means a story collection or an anthology of short stories.

After nouns like сборник, Russian often uses the genitive to show what the collection consists of.

So:

• сборник стихов = a collection of poems
• сборник статей = a collection of articles
• сборник рассказов = a collection of stories

This is a very common pattern in Russian.

Because о котором я раньше даже не слышала is a relative clause describing сборник рассказов.

In English, this is like which I had never even heard of before.
Russian normally separates this kind of descriptive relative clause with a comma.

Because the expression is слышать о ком-то / о чём-то = to hear of someone/something or to hear about someone/something.

Inside the relative clause, the missing phrase is:

я раньше даже не слышала о сборнике

Since слышать here requires о + prepositional case, the relative pronoun also has to appear in that form:

• который is the dictionary form
• masculine singular prepositional after о becomes о котором

So о котором means about which or more naturally in English here, which ... of.

Because the main noun in the phrase is сборник.
The word рассказов only tells you what kind of collection it is.

So grammatically, the clause describes the collection, not the stories:

• сборник = masculine singular
• therefore о котором = masculine singular

If the head noun were feminine, you would get something like о которой instead.

Here, слышать о does not mean literal physical hearing. It means to have heard of or to know of the existence of something.

So:

• Я не слышала об этом = I hadn’t heard about it / I hadn’t heard of it
• Я раньше даже не слышала = I hadn’t even heard of it before

The word раньше means earlier / before, and in this sentence it points to the time before she recommended it.

Даже means even. It adds emphasis and shows surprise.

Compare:

• я раньше не слышала = I hadn’t heard of it before
• я раньше даже не слышала = I hadn’t even heard of it before

So the speaker is emphasizing that the book was completely unknown to her.

Because the speaker is female. In the past tense, Russian verbs agree in gender with the subject.

So:

• я ... не слышала = a female speaker
• я ... не слышал = a male speaker

This is one of the things Russian past tense marks that English does not.

No, Russian word order is fairly flexible, but this version sounds natural.

• Вдобавок at the beginning sets up the idea of in addition
• мне comes before сборник рассказов, which is a very normal order for a short pronoun
• the relative clause comes right after the noun phrase it describes

You could move words around, but the sentence as written is smooth and standard.