В магазине мне понравились сандалии, но я всё-таки выбрала туфли.

Because понравиться works differently from English to like.

In Russian, the person who experiences the feeling is in the dative case:

• мне = to me

The thing that causes the feeling is the grammatical subject:

• сандалии = the sandals

So the structure is closer to:

• The sandals pleased me
• literally: To me, the sandals were pleasing

That is why:

• мне is in the dative
• сандалии is the subject
• понравились agrees with сандалии

This is one of the most important patterns to learn with нравиться / понравиться.

Because сандалии is plural, and the verb in the past tense agrees with the subject in number.

Compare:

• мне понравилась книга = I liked the book
• мне понравилось платье = I liked the dress
• мне понравились сандалии = I liked the sandals

So:

• singular feminine subject → понравилась
• singular neuter subject → понравилось
• plural subject → понравились

Here the subject is сандалии, so the verb must be plural: понравились.

It is in the nominative plural.

That may feel surprising to an English speaker, because in English the thing you like is an object:

• I liked the sandals

But with понравиться, the thing liked is actually the subject:

• сандалии понравились мне

So сандалии is nominative, not accusative.

Not necessarily. Russian often uses the plural for items of footwear when talking about a pair.

So:

• сандалии usually means sandals / a pair of sandals
• туфли usually means shoes / a pair of shoes

This is very natural in Russian. English does something similar with words like pants or glasses, though not usually with shoes.

Singular forms do exist:

• сандалия = one sandal
• туфля = one shoe

But in normal everyday speech, when talking about buying or choosing footwear, Russian very often uses the plural.

Because туфли here is the direct object of выбрала, so it is in the accusative plural.

For inanimate plural nouns, the accusative form is usually the same as the nominative.

So:

• nominative plural: туфли
• accusative plural: туфли

That is why the form does not change.

If the noun were animate, the accusative plural would often look like the genitive plural instead.

In the past tense, Russian verbs show gender in the singular.

So:

• я выбрал = I chose, if the speaker is male
• я выбрала = I chose, if the speaker is female

Here выбрала tells you that the speaker is female.

This is a very common feature of Russian past tense:

• masculine: no final -а
• feminine: -а
• neuter: -о
• plural: -и

Всё-таки adds a nuance like:

• still
• all the same
• nevertheless
• in the end
• after all

In this sentence, it shows a contrast between two ideas:

• the speaker liked the sandals
• but despite that, she chose the shoes

So всё-таки suggests something like:

• but I still chose the shoes
• but in the end I chose the shoes

It often gives the sentence a feeling of final decision despite some competing factor.

The difference is mainly aspect.

• нравиться = imperfective
• понравиться = perfective

Here понравились is perfective, so it refers to a completed reaction or impression:

• I found the sandals appealing
• I liked them when I saw/tried them

If you said мне нравились сандалии, it would usually sound more like:

• I liked the sandals
• I used to like the sandals
• I was liking the sandals / found them nice over a period of time

In a shopping context, понравились is very natural because it describes that moment of impression: the sandals caught her fancy, but she ended up choosing something else.

Because в plus the prepositional case is used to express location: in or at a place.

• магазин = store/shop
• в магазине = in the store / at the store

Here it tells you where the situation happened.

Compare:

• в магазин = to the store, into the store (motion toward)
• в магазине = in the store (location)

So the sentence is talking about what happened while she was in the store.

Yes. Russian word order is flexible, and changing it often changes emphasis, not the core meaning.

For example:

• В магазине мне понравились сандалии, но я всё-таки выбрала туфли.
• Мне в магазине понравились сандалии, но я всё-таки выбрала туфли.
• Сандалии мне понравились в магазине, но я всё-таки выбрала туфли.

All of these can be possible, but they highlight different things:

• В магазине first sets the scene
• мне earlier can emphasize the personal reaction
• сандалии earlier can emphasize what was liked

The original sentence sounds natural and starts by placing us in the store, which is a common way to frame the situation.

Но means but and introduces a clear contrast.

The contrast is:

• she liked the sandals
• she chose the shoes instead

That makes но the natural conjunction.

In Russian, а can also connect contrasting ideas, but но is stronger and more directly like English but. In this sentence, the contrast is strong enough that но fits very well.