Hon vill hellre handla på marknaden än i matbutiken.

Because hon is the subject form of she.

In Hon vill hellre handla ..., hon is the person doing the action, so Swedish uses hon.

• hon = she (subject)
• henne = her (object)

Compare:

• Hon handlar. = She shops.
• Jag ser henne. = I see her.

Because vill is a modal verb, and modal verbs in Swedish are normally followed by the bare infinitive.

So:

• hon vill handla = she wants to shop

Not:

• hon vill att handla ❌

Other common modal verbs work the same way:

• kan handla = can shop
• ska handla = will/is going to shop
• måste handla = must shop

So vill + infinitive is the normal pattern.

Hellre ... än ... is the standard way to say rather ... than ... in Swedish.

In this sentence:

• hellre handla på marknaden än i matbutiken = rather shop at the market than in the grocery store

So:

• hellre = rather / preferably
• än = than

This pattern is very common:

• Jag stannar hellre hemma än går ut.
• Vi åker hellre tåg än bil.

It expresses preference between two alternatives.

Because in a normal Swedish main clause, the finite verb usually comes in the second position, and sentence adverbs like hellre often come after that verb.

So the order is:

• Hon — subject
• vill — finite verb
• hellre — adverb
• handla — infinitive

This is very typical Swedish word order.

Compare:

• Hon vill hellre handla ...
• Jag ska gärna hjälpa dig.
• De kan inte komma.

The finite verb comes early, and adverbs often follow it.

Yes, handla can mean more than one thing.

In this sentence, it clearly means:

• to shop
• often especially to buy food/groceries

For example:

• Jag ska handla. = I’m going shopping / I’m going to buy groceries.

But handla can also mean to be about in another context:

• Filmen handlar om kärlek. = The film is about love.

So context matters. Here, because of på marknaden and i matbutiken, it means shop / buy groceries.

This is mainly about Swedish preposition usage.

• på marknaden = at the market
• i matbutiken = in the grocery store

Swedish often uses på for places seen as an area, venue, event, or public setting:

• på marknaden
• på jobbet
• på restaurang
• på landet

Swedish often uses i for being inside an enclosed place:

• i butiken
• i huset
• i köket

So the contrast here sounds natural:

• at the market
• in the grocery store

Prepositions do not always match English exactly, so this is something learners usually need to get used to phrase by phrase.

Because Swedish usually puts the definite article at the end of the noun.

So:

• en marknad = a market

• marknaden = the market

• en matbutik = a grocery store
• matbutiken = the grocery store

This ending works like English the.

So instead of a separate word before the noun, Swedish often attaches definiteness to the noun itself.

Because Swedish normally uses a suffix for definiteness instead of a separate article.

So:

• marknaden already means the market
• matbutiken already means the grocery store

That final -en is doing the job of English the.

A separate definite word like den is only used in certain situations, especially with adjectives:

• marknaden = the market
• den stora marknaden = the big market

So in your sentence, no extra word is needed.

Because Swedish often leaves out repeated words when they are understood from context.

The full idea is:

• Hon vill hellre handla på marknaden än handla i matbutiken.

But repeating handla sounds unnecessary, so Swedish normally says:

• Hon vill hellre handla på marknaden än i matbutiken.

English does the same thing:

• She would rather shop at the market than in the grocery store.

You understand that shop applies to both parts.

Yes, but the meaning changes slightly.

• Hon vill hellre handla på marknaden än i matbutiken
  = She wants to shop at the market rather than in the grocery store.

• Hon handlar hellre på marknaden än i matbutiken
  = She prefers shopping / shops preferably at the market rather than in the grocery store.

The version with vill emphasizes wanting or intention.
The version without vill states more directly what she prefers or usually does.

When you explicitly compare two alternatives, yes, än is the normal word.

Examples:

• Jag dricker hellre te än kaffe.
• Vi går hellre än åker bil.
• Hon vill hellre stanna hemma än gå ut.

But sometimes the second part is left out if it is obvious:

• Jag tar hellre te. = I’d rather have tea.

So än appears when the sentence actually includes the comparison.

It is a compound noun:

• mat = food
• butik = shop/store
• matbutik = grocery store / food shop
• matbutiken = the grocery store

Compound nouns are extremely common in Swedish. The last part is usually the main noun, and the first part modifies it.

Other examples:

• bokhandel = bookshop
• stormarknad = supermarket
• köksbord = kitchen table

So matbutiken is a very typical Swedish compound.