Skadan finns på dörrkarmen och låset.

Skadan is the definite singular form of en skada (damage, the damage).

• en skada = a damage / damage
• skadan = the damage

So this sentence is talking about specific damage that is already known from the context.

The ending works like this:

• en skada
• skadan

This is very common in Swedish: instead of using a separate word like the, Swedish usually adds the definiteness to the end of the noun.

Finns is the present tense of finnas, which often means to exist, to be found, or to be located.

In this sentence, Skadan finns på dörrkarmen och låset means something like:

• The damage is on the door frame and the lock
• more literally: The damage is found on the door frame and the lock

A native English speaker may expect är, but Swedish often uses finns when pointing out that something is present somewhere.

Compare:

• Det finns en katt i huset. = There is a cat in the house.
• Skadan finns på dörrkarmen. = The damage is on the door frame.

Using är here would sound less natural.

Here, på means on.

So:

• på dörrkarmen = on the door frame
• på låset = on the lock

This is a normal choice when talking about damage on a surface or on a part of something.

English and Swedish often match here:

• on the wall = på väggen
• on the door = på dörren
• on the lock = på låset

Because the sentence refers to the door frame and the lock, not just any door frame or any lock.

• dörrkarm = door frame
• dörrkarmen = the door frame
• lås = lock
• låset = the lock

Swedish usually marks definiteness directly on the noun:

• en dörrkarm → dörrkarmen
• ett lås → låset

So the phrase means:

• på dörrkarmen och låset
• on the door frame and the lock

Because the nouns belong to different grammatical genders.

1. dörrkarm is an en-word

• en dörrkarm
• definite singular: dörrkarmen

2. lås is an ett-word

• ett lås
• definite singular: låset

So the endings reflect noun gender:

• en-word → usually -en in the definite singular
• ett-word → usually -et in the definite singular

This is one of the most important patterns in Swedish grammar.

Yes. Swedish very often combines nouns into one compound word.

Here:

• dörr = door
• karm = frame
• dörrkarm = door frame

This is extremely common in Swedish. English sometimes uses two words where Swedish uses one:

• door handle → dörrhandtag
• car key → bilnyckel
• bedroom door → sovrumsdörr

So dörrkarmen is just the definite form of the compound noun dörrkarm.

The basic structure is:

• Skadan = subject
• finns = verb
• på dörrkarmen och låset = place/location phrase

So:

Skadan / finns / på dörrkarmen och låset.

This is normal Swedish main-clause word order: subject + verb + other information.

A learner may notice that it looks quite similar to English here, which is helpful.

Yes, the natural reading is that the damage is on both:

• the door frame
• and the lock

So the damage affects both parts.

If a speaker wanted to be extra clear, they might also phrase it in a more expanded way, but this sentence already strongly suggests both.

Usually not in this sentence.

• på = on
• i = in

Since the damage is being described as being on the surface or on those parts, på is the natural choice.

Using i would suggest something more like inside the frame or inside the lock, which changes the meaning.

So for visible physical damage on those parts, på is the right preposition.

Yes, if you are talking about the damages or the damaged areas in the plural, you could use skadorna.

Forms:

• en skada = a damage
• skadan = the damage
• skador = damages / areas of damage
• skadorna = the damages / the areas of damage

So:

• Skadan finns på dörrkarmen och låset. = The damage is on the door frame and the lock.
• Skadorna finns på dörrkarmen och låset. = The damages are on the door frame and the lock.

That said, Swedish often uses the singular skadan when referring to the damage as one issue or one set of damage.

It is understandable and acceptable, but depending on context, a Swede might also say things like:

• Det finns en skada på dörrkarmen och låset.
• Det är skador på dörrkarmen och låset.
• Dörrkarmen och låset har skador.

The original sentence is fine, especially if the damage has already been identified and you are now stating where it is.

So Skadan finns på dörrkarmen och låset works well when the listener already knows which damage you mean.