Раз уж я всё равно пришла в книжный, я непременно куплю подарок бабушке.

Раз уж is a conversational connector meaning something like:

• since
• seeing as
• given that
• if I’m already at the point where...

In this sentence, Раз уж я всё равно пришла в книжный... means:

• Since I came to the bookstore anyway...
• Seeing as I’m already at the bookstore...

It often adds a feeling of “well, since that’s already the case”.

Yes, всё равно can mean it’s all the same or I don’t care, but it also very often means anyway.

Here it means:

• I came anyway
• I came in any case
• I’m here already regardless

So Раз уж я всё равно пришла в книжный is roughly:

• Since I came to the bookstore anyway...
• Since I’m here already anyway...

This is a very common use of всё равно in everyday Russian.

Because the speaker is female.

In the past tense, Russian verbs agree with gender in the singular:

• я пришёл = I came (male speaker)
• я пришла = I came (female speaker)
• я пришло = neuter, not used for normal people
• мы пришли = we came

So пришла tells you the speaker is a woman or girl.

This is a very common colloquial shortening.

Книжный literally means book-related or bookstore when used by itself. It comes from книжный магазин = bookstore / bookshop.

So:

• в книжный магазин = full form
• в книжный = natural shortened form in speech

Russian often does this with store names:

• в продуктовый = to the grocery store
• в обувной = to the shoe store
• в книжный = to the bookstore

It sounds normal and natural in conversation.

Because в with motion toward a place usually takes the accusative.

Here the idea is came into/to the bookstore, so we use motion:

• в книжный = to the bookstore

Compare:

• Я пришла в книжный. = I came to the bookstore.
  (motion → accusative)

• Я была в книжном. = I was in the bookstore.
  (location → prepositional)

So:

• в книжный = destination
• в книжном = location

Непременно means definitely, certainly, for sure.

So:

• я непременно куплю = I will definitely buy

It is very close to обязательно, and in many sentences they can replace each other.

However, there is a slight stylistic difference:

• обязательно is extremely common and neutral
• непременно can sound a bit more emphatic, determined, or slightly more literary

Here непременно gives the sense:

• I’m definitely going to buy a present for my grandmother
• I’ll make sure to buy one

Куплю is the perfective future of купить.

Russian uses:

• imperfective future: буду покупать = I will be buying / I will buy habitually / process-focused
• perfective future: куплю = I will buy / I’ll get it done

Here the speaker means a single completed action:

• I will buy a present

So куплю is exactly what Russian normally uses here.

If you said буду покупать, it would sound more like emphasis on the process, repetition, or ongoing action, which is not the main idea.

Because Russian commonly uses the dative case to mark the person who receives something.

So:

• подарок бабушке = a present for grandma
• literally: a present to grandma

This is very natural Russian.

You can also say для бабушки, but it can sound a little more explicit or sometimes less idiomatic depending on context. In many cases, Russian prefers the dative with nouns like подарок:

• купить подарок маме
• принести цветы сестре
• написать письмо другу

So подарок бабушке is the most natural phrasing here.

Бабушке is dative singular.

The base form is:

• бабушка = grandmother

In the dative singular, it becomes:

• бабушке = to/for grandmother

This is because the sentence expresses the recipient of the gift:

• куплю подарок бабушке = I’ll buy a present for my grandmother

For many feminine nouns ending in -а / -я, the dative singular often ends in -е:

• мама → маме
• сестра → сестре
• бабушка → бабушке

Because the sentence has two clauses:

1. Раз уж я всё равно пришла в книжный
2. я непременно куплю подарок бабушке

The first clause gives the reason/background:

• Since I came to the bookstore anyway...

The second clause gives the main result/decision:

• ...I’ll definitely buy a present for my grandmother.

Russian uses a comma here just as English often separates a dependent clause from the main clause.

The current word order is natural and expressive, but Russian word order is flexible.

Current version:

• Раз уж я всё равно пришла в книжный, я непременно куплю подарок бабушке.

This sounds like:

• first, the circumstance: since I’m here anyway
• then, the decision: I’ll definitely buy...

You could change the order of some words for emphasis, for example:

• Раз уж я пришла в книжный всё равно, ...
  Grammatically possible, but less natural.

• ...я куплю бабушке подарок.
  Also possible; this puts a slightly different emphasis on бабушке.

Russian word order often reflects focus and emphasis, not just grammatical structure. The version given is very natural.

Yes, somewhat.

Раз уж is common in everyday speech and informal writing. It has a natural, conversational feel. It is not wrong in more neutral contexts, but it is less formal than a plain поскольку or так как.

Compare:

• Раз уж я всё равно пришла... = conversational, natural
• Поскольку я всё равно пришла... = more formal/bookish
• Так как я всё равно пришла... = neutral, standard

So this sentence sounds like something a person would naturally say in conversation.

Yes, that implication is quite possible.

The combination of раз уж and всё равно suggests reasoning like:

• Well, I’m here already anyway, so I might as well buy the gift.

So the sentence can carry the feeling that:

• being at the bookstore creates a convenient opportunity
• the speaker is making a decision based on the current situation

That nuance is stronger than in a simple sentence like:

• Я куплю подарок бабушке. = I’ll buy a present for my grandmother.

The original sentence sounds more like:

• Since I’m already here, I’ll definitely do it now.