Syksyllä käytän villatakkia kotona, kun en halua laittaa takkia päälle.

Syksyllä is the usual Finnish way to say in autumn / during the autumn.

It is in the adessive case (-lla / -llä), which is often used for:

• time expressions
• seasons
• parts of the day in some contexts

Examples:

• kesällä = in summer
• talvella = in winter
• syksyllä = in autumn

So even though -lla/-llä often means on or at, with seasons it usually means during that season.

Villatakkia is in the partitive singular.

With the verb käyttää in the sense to wear / to use, Finnish very often uses the partitive object, especially when talking about clothing in a general way.

So:

• käytän villatakkia = I wear a wool cardigan
• käytän hattua = I wear a hat
• käytän silmälaseja = I wear glasses

This does not mean the cardigan is only partly used in a literal sense. It is just the normal object form here.

Villatakki is a compound word:

• villa = wool
• takki = coat, jacket, cardigan, outer garment depending on context

So villatakki means a wool cardigan / wool jacket / wool sweater-like jacket.
In this sentence it most naturally means cardigan.

Finnish uses compound words very freely, so this is very normal:

• talvitakki = winter coat
• sadetakki = raincoat
• nahkatakki = leather jacket

Kotona means at home.

It is one of the common location forms of koti:

• koti = home
• kotona = at home
• kotiin = to home / homeward
• kotoa = from home

So:

• Olen kotona. = I am at home.
• Menen kotiin. = I am going home.
• Tulen kotoa. = I come from home.

In your sentence, kotona shows the location where the action happens.

Kun can mean several things, including:

• when
• as
• sometimes something close to because

In this sentence, it most naturally means when or whenever:

• Syksyllä käytän villatakkia kotona, kun en halua laittaa takkia päälle.
• In autumn I wear a cardigan at home when I don’t want to put on a coat.

So it introduces the situation in which the speaker does this.

Context is what tells you which meaning kun has.

Finnish negative verbs work differently from English.

The negative verb is conjugated, and the main verb appears in a special short form.

Here:

• en = I do not
• halua = the negative form of haluta for this structure

Compare:

• haluan = I want
• en halua = I do not want

More examples:

• minä tiedän = I know
• minä en tiedä = I do not know

So en halua is completely regular Finnish negation.

Laittaa ... päälle means to put ... on in the sense of clothing.

So:

• laittaa takki päälle = put the coat on
• laittaa kengät päälle is less usual; with shoes people more often say laittaa kengät jalkaan
• laittaa paita päälle = put on a shirt

Here päälle literally relates to onto/on top, but in clothing expressions it works like on in English put on.

So:

• laittaa takkia päälle = to put on a coat

This is a very common Finnish structure.

Here takkia is in the partitive.

A very important rule for learners is:

• In a negative clause, the object is usually in the partitive.

Since the sentence says:

• en halua = I do not want

the object inside that idea appears as partitive:

• en halua laittaa takkia päälle

If the sentence were positive, you could more naturally get:

• Haluan laittaa takin päälle. = I want to put the coat on.

So takkia is largely explained by the negation.

They refer to two different kinds of garments in this sentence:

• villatakki = a wool cardigan / indoor warm layer
• takki = a coat or jacket, usually more like outerwear

So the sentence contrasts:

• wearing a cardigan at home
• not wanting to put on a coat

Finnish often uses a more specific compound word first and then a more general word later if the meanings are clearly different from context.

Yes, Finnish word order is fairly flexible.

This sentence starts with Syksyllä to set the time frame first:

• Syksyllä = In autumn

That is very natural in Finnish. It gives the sentence a topic right away.

Other possible orders could be:

• Käytän syksyllä villatakkia kotona...
• Kotona käytän syksyllä villatakkia...

These are all possible, but they shift the emphasis slightly:

• Syksyllä first emphasizes the season
• Kotona first emphasizes the location
• käytän first sounds a bit more neutral or direct

So the original order is natural and idiomatic.

Both, depending on context.

The verb käyttää can mean:

• to use
• to wear

Examples:

• Käytän tietokonetta. = I use a computer.
• Käytän villatakkia. = I wear a cardigan.

So in this sentence, because the object is a piece of clothing, käytän means I wear.

Yes, but the wording changes a little.

Common options include:

• laittaa takki päälle = put on a coat
• pukea takki päälle = put a coat on
• pukea takki ylle = a bit more literary/formal
• pukeutua takkiin = dress oneself in a coat

In everyday speech, laittaa ... päälle is very common and natural.

So the sentence sounds very normal as it is.