Har du sett min handduk? Den låg på sängen i morse.

In a yes/no question in Swedish, the finite verb usually comes first.

• Du har sett min handduk. = You have seen my towel.
• Har du sett min handduk? = Have you seen my towel?

So Swedish works a lot like English here: you move the auxiliary verb to the front to form the question.

It is the present perfect.

It is made with:

• har = have
• sett = seen

So:

• Har du sett min handduk? = Have you seen my towel?

This tense is often used when something in the past is relevant now. In this sentence, the speaker is asking about the towel because it is missing now.

Both can be possible in Swedish, but they give slightly different feelings.

• Har du sett min handduk? = Have you seen my towel?
  This focuses on the current situation: the towel is missing now.
• Såg du min handduk? = Did you see my towel?
  This sounds more like asking about a specific moment in the past.

Because the towel matters in the present, har sett is very natural here.

In Swedish, when you use a possessive like min, din, hans, hennes, vår, etc., the noun usually stays in its indefinite form.

So you say:

• min handduk = my towel
• din bok = your book

Not:

• min handduken

This is different from English, where the noun form does not change.

Den refers back to handduk.

Since handduk is an en-word, the matching pronoun is den.

• en handduk → den
• ett bord → det

So:

• Den låg på sängen = It was lying on the bed

If the noun had been an ett-word, Swedish would use det instead.

Yes, mostly. Swedish nouns have grammatical gender, usually called en-words and ett-words.

• en handduk
• definite form: handduken
• pronoun: den

There are some patterns, but in many cases learners simply need to learn the noun together with its article:

• en handduk
• ett hus
• en stol

That is the safest way.

Låg is the past tense of ligga, which means to lie or to be lying.

So:

• Den låg på sängen = It was lying on the bed / It was on the bed

Swedish often uses position verbs more specifically than English:

• ligga = lie
• stå = stand
• sitta = sit

English often just says was, but Swedish often prefers the more specific verb.

So Den låg på sängen sounds more natural than Den var på sängen.

Yes. Låg is the past tense of ligga, and it is irregular.

The forms are:

• infinitive: ligga = to lie
• present: ligger = is lying
• past: låg = lay / was lying
• supine: legat = lain

So this is just a verb form you need to learn.

This is a very common question.

• ligga = to lie, to be lying somewhere
  It describes a position.
• lägga = to lay, to put something down
  It describes an action.

Examples:

• Handduken ligger på sängen. = The towel is lying on the bed.
• Jag lägger handduken på sängen. = I put the towel on the bed.

In your sentence, the towel is already there, so låg from ligga is correct.

Because på means on, while i means in.

• på sängen = on the bed
• i sängen = in the bed

For a towel resting on top of the bed, på sängen is the natural choice.

If someone is under the covers, you would more likely say i sängen.

Sängen is the definite form: the bed.

• en säng = a bed
• sängen = the bed

Here, the speaker means a specific bed, probably one both people understand from the situation. That is why Swedish uses the definite form.

So:

• på sängen = on the bed

I morse means this morning, referring to the morning of today.

Examples:

• Jag åt frukost i morse. = I ate breakfast this morning.
• Den låg på sängen i morse. = It was lying on the bed this morning.

It is used for something earlier today, not for mornings in general.

They mean different things.

• i morse = this morning
• på morgonen = in the morning / during the morning

So in your sentence, i morse is correct because the speaker means earlier today.

Compare:

• Jag duschade i morse. = I showered this morning.
• Jag brukar duscha på morgonen. = I usually shower in the morning.

Yes, that is strongly suggested.

The speaker says it was on the bed this morning, which implies that now it is missing or not there anymore. That is why the first sentence asks:

• Har du sett min handduk?

So the two sentences work together:

1. Have you seen my towel?
2. It was on the bed this morning.

It would be:

• Du har sett min handduk. = You have seen my towel.

That is the normal statement word order. In the actual sentence, Swedish changes the order to make it a yes/no question:

• Har du sett min handduk?

So this is a good example of how Swedish switches word order in questions.