Даже в будничной одежде она выглядит аккуратно, а полосатый кардиган ей очень идёт.

Даже means even.

In Даже в будничной одежде она выглядит аккуратно, it adds the idea that even when she is wearing ordinary/everyday clothes, she still looks neat.

So it highlights something a little surprising or noteworthy:

• Она выглядит аккуратно = She looks neat.
• Даже в будничной одежде = Even in everyday clothes.

Одежде is in the prepositional case.

The phrase в одежде here means in clothing / wearing clothing of a certain kind. After в in this kind of static meaning (location, state, circumstance), Russian commonly uses the prepositional case.

So:

• одежда = clothing
• в одежде = in clothing / dressed in clothing
• в будничной одежде = in everyday clothes

The adjective also matches:

• будничная одежда → nominative
• в budничной одежде → prepositional

Будничный means something like everyday, ordinary, not festive, plain.

In this sentence, будничной одежде suggests ordinary clothes, as opposed to dressy or special clothes.

It is similar to повседневный, but there is a slight nuance:

• повседневный = everyday, daily-use, neutral
• будничный = everyday, ordinary, routine, sometimes with a slightly plain or non-special feel

So будничная одежда sounds a bit more like regular, non-fancy clothes.

Аккуратно is an adverb, because it describes how she looks.

Literally, аккуратный / аккуратно can mean things like:

• neat
• tidy
• well-kept
• carefully arranged

In this sentence, она выглядит аккуратно means:

• She looks neat
• She looks well put together
• She looks tidy

This is a very natural use in Russian. It does not mean she is “doing something carefully” here; it means her appearance is neat.

Выглядит is the 3rd person singular present tense of выглядеть:

• выглядеть = to look, to appear

So:

• она выглядит = she looks

This verb is commonly followed by:

• an adverb: выглядит аккуратно = looks neat
• an adjective-like description in some constructions
• age/condition expressions: выглядит молодо = looks young

It is an imperfective verb, and in the present tense it refers to a current general impression.

А often connects two related ideas while also giving a slight contrast or shift of focus.

Here:

• Даже в будничной одежде она выглядит аккуратно = Even in everyday clothes, she looks neat,
• а полосатый кардиган ей очень идёт = and/as for the striped cardigan, it suits her very well.

Using а feels natural because the sentence moves from:

1. her overall appearance
2. to one specific item of clothing

So а is not always a strong but. Very often it means something like:

• and
• while
• whereas
• as for

In this sentence, а is best understood as a smooth contrastive link.

Yes, идти literally means to go / to walk, but Russian often uses it in other expressions too.

In clothing descriptions, идти кому-то means:

• to suit someone
• to look good on someone
• to become someone

So:

• кардиган ей идёт = the cardigan suits her / looks good on her

This is a very common expression in Russian:

• Тебе идёт этот цвет. = This color suits you.
• Ей очень идёт эта причёска. = That hairstyle suits her very much.

So here идёт is not about physical movement at all.

Because the expression is идти кому? — to suit whom?

That means the person who is being suited is put in the dative case.

So:

• она = she
• ей = to her

In this sentence:

• полосатый кардиган ей очень идёт
• literally: The striped cardigan goes to her very well
• naturally: The striped cardigan suits her very well

This is just how the Russian expression works:

• Мне идёт синий цвет. = Blue suits me.
• Тебе идёт это платье. = That dress suits you.

Because полосатый кардиган is the grammatical subject of идёт.

In the expression что-то идёт кому-то, the thing that suits someone is the subject:

• кардиган идёт ей = the cardigan suits her

So:

• полосатый кардиган = nominative singular masculine
• ей = dative singular

That is why it is полосатый кардиган, not a different case form.

Полосатый means striped.

It comes from полоса = stripe, band.

So:

• полосатый кардиган = a striped cardigan

It is a regular adjective and agrees with кардиган:

• masculine singular nominative: полосатый
• because кардиган is masculine singular nominative

Yes, Russian word order is flexible, but changing it changes the focus or emphasis.

The original sentence:

• Даже в будничной одежде она выглядит аккуратно, а полосатый кардиган ей очень идёт.

This sounds natural and balanced:

1. first the circumstance: even in everyday clothes
2. then the person and verb: she looks neat
3. then a second comment: the striped cardigan suits her very well

Other orders are possible, for example:

• Она даже в будничной одежде выглядит аккуратно...
• Ей очень идёт полосатый кардиган...

These are grammatical, but the emphasis shifts:

• putting она earlier highlights her
• putting ей очень идёт earlier highlights the fact that it really suits her

So the original order is not the only possible one, but it is a very natural choice.