Den tionde maj vill hon ordna en liten fest för sina vänner.

Both are possible, but they have different word order because of a basic Swedish rule: the finite verb comes second in main clauses.

• Neutral order: Hon vill ordna en liten fest för sina vänner den tionde maj.
• If you move the time expression to the front for emphasis or to set the scene, the verb must still stay in second position:
  • Den tionde maj vill hon ordna en liten fest för sina vänner.

So vill hon is not a question here. It is just normal Swedish V2 word order after a fronted time expression.

This is the standard way to say a date in Swedish:

• den = the
• tionde = tenth
• maj = May

So den tionde maj literally means the tenth of May.

A few useful notes:

• tio = ten
• tionde = tenth

Swedish uses the ordinal number for dates, not the cardinal number.

You will also often see dates written with numerals, for example:

• den 10 maj
• sometimes simply 10 maj

In Swedish, dates are often used without a preposition.

So Swedish says:

• Den tionde maj...
• Vi ses den tionde maj.

where English might say:

• On the tenth of May...
• We’ll meet on the tenth of May.

This is very normal in Swedish. English often needs on, but Swedish often does not.

Because in Swedish, months are not normally capitalized.

That also applies to:

• days of the week
• languages
• many nationality words

So:

• maj = May
• måndag = Monday
• svenska = Swedish

This is different from English, where these words are usually capitalized.

Ordna means something like:

• arrange
• organize
• set up

So ordna en liten fest means organize/arrange a small party.

It suggests that she is planning it or making it happen.

Compare:

• ordna en fest = organize a party
• ha en fest = have a party

In many contexts, both could work, but ordna focuses more on the act of arranging it.

Because fest is an en-word in Swedish:

• en fest = a party

Adjectives must agree with the noun, so:

• en liten fest = a small party

If the noun were an ett-word, you would use litet instead:

• ett litet hus = a small house

So the pattern is:

• en noun → liten
• ett noun → litet

Because fest is singular here.

• en liten fest = a small party
• små fester = small parties

So:

• liten is used with singular common-gender nouns
• små is used in the plural

This adjective is a bit irregular, which is why it is worth memorizing:

• en liten fest
• ett litet hus
• små fester
• den lilla festen

Because sina is a reflexive possessive. It refers back to the subject of the clause.

Here the subject is hon:

• hon = she

So:

• sina vänner = her own friends

This is exactly the situation where Swedish uses sin / sitt / sina.

Compare:

• Hon vill ordna en liten fest för sina vänner.
  = She wants to organize a small party for her own friends.

• Hon vill ordna en liten fest för hennes vänner.
  = She wants to organize a small party for her friends, where her refers to some other female person, not normally the subject herself.

So sina is the natural choice here.

Because the possessive must agree with the thing being possessed, not with the owner.

The possessed noun here is:

• vänner = friends

That is plural, so Swedish uses sina.

The reflexive possessive forms are:

• sin for singular en-words
• sitt for singular ett-words
• sina for plural nouns

Examples:

• hon älskar sin hund = she loves her dog
• hon säljer sitt hus = she sells her house
• hon träffar sina vänner = she meets her friends

Yes. Here för means for in the sense of for the benefit of or for someone.

So:

• en fest för sina vänner = a party for her friends

This is the natural preposition in this sentence.

It does not mean that the friends necessarily receive the party as a gift; it simply means the party is intended for them, or being arranged with them as the guests.

A simple breakdown is:

• Den tionde maj = time expression
• vill = finite verb
• hon = subject
• ordna = infinitive
• en liten fest = object
• för sina vänner = prepositional phrase

So the sentence structure is roughly:

Time + verb + subject + infinitive + object + prepositional phrase

A more neutral version with the subject first would be:

• Hon vill ordna en liten fest för sina vänner den tionde maj.

Both are correct; the original just puts the date first.