Hana grunar að lykillinn sé enn í handtöskunni.

Because gruna is used here in an impersonal construction. The person who has the suspicion is not put in the nominative case.

• hún = nominative she
• hana = accusative her

So Hana grunar ... literally uses hana, even though in English we translate it as she suspects ... or she suspects that ...

This is similar to other Icelandic verbs where English uses a normal subject, but Icelandic uses another case instead, such as:

• Mig langar = I want
• Mig vantar = I need / I am lacking

So here, hana is correct because gruna takes the experiencer in the accusative.

Grunar is the present tense of að gruna.

In this kind of sentence, it means something like:

• to suspect
• to have a suspicion
• to think something may be the case

So Hana grunar að ... means she suspects that ...

A useful pattern to remember is:

• Mig grunar að ... = I suspect that ...
• Þig grunar að ... = you suspect that ...
• Hana grunar að ... = she suspects that ...

Here að means that and introduces a subordinate clause:

• Hana grunar = she suspects
• að lykillinn sé enn í handtöskunni = that the key is still in the handbag

So the sentence structure is:

• main clause: Hana grunar
• subordinate clause: að lykillinn sé enn í handtöskunni

Be careful: að can also mean to before an infinitive, but not here. In this sentence it is the conjunction that.

Because lykillinn means the key, while lykill means a key or just key in a dictionary form.

Icelandic usually adds the definite article to the end of the noun:

• lykill = key
• lykillinn = the key

So if the English meaning is the key, Icelandic naturally uses lykillinn.

Sé is the subjunctive form of vera (to be).
Er is the normal indicative present tense.

Here Icelandic uses the subjunctive because the clause expresses something suspected, uncertain, or not presented as a confirmed fact.

Compare:

• Lykillinn er í handtöskunni. = The key is in the handbag.
  → presented as a fact
• Hana grunar að lykillinn sé í handtöskunni. = She suspects that the key is in the handbag.
  → not confirmed, just suspected

So sé helps show that this is a possibility or belief, not an established fact.

No. Að by itself does not automatically require the subjunctive.

What matters is the meaning of the main clause. Verbs involving:

• doubt
• suspicion
• uncertainty
• wishes
• indirect or non-factual statements

often lead to the subjunctive in the subordinate clause.

So in this sentence, the subjunctive comes mainly from grunar and the idea of suspicion, not just from the word að.

Because í can take either:

• accusative for motion into
• dative for location in

Here the meaning is location: the key is in the handbag, not moving into it. So Icelandic uses the dative.

That is why we get:

• í handtösku / í handtöskuna type forms for motion, depending on structure
• í handtöskunni for location in the handbag

So:

• Lykillinn er í handtöskunni. = The key is in the handbag.
• Hún setti lykilinn í handtöskuna. = She put the key into the handbag.

Handtöskunni is the dative singular definite form of handtaska (handbag).

Breaking it down:

• handtaska = handbag
• handtöskunni = in the handbag / to the handbag depending on the preposition and context

The form changes because Icelandic nouns show:

• case
• number
• definiteness

Here it is:

• singular
• definite = the handbag
• dative, because it follows í in a location meaning

So the ending tells you a lot of grammar at once.

Enn means still in this sentence.

So:

• Lykillinn sé enn í handtöskunni = the key is still in the handbag

It suggests that the key may have been there before and may still be there now.

Be aware that enn can also mean yet in some contexts, but here still is the natural meaning.

Yes, this is normal and natural.

The subordinate clause has a standard order:

• lykillinn = subject of the subordinate clause
• sé = verb
• enn = adverb
• í handtöskunni = prepositional phrase

So:

• að lykillinn sé enn í handtöskunni

is a straightforward way to say that the key is still in the handbag.

The subject of that subordinate clause is lykillinn.

Even though the main clause is impersonal (hana grunar), the subordinate clause is ordinary:

• lykillinn = subject
• sé = verb

So grammatically:

• main clause: hana is in the accusative with the impersonal verb grunar
• subordinate clause: lykillinn is the nominative subject of sé

In some contexts, you may hear or see the indicative after að, but in careful standard Icelandic, sé is the expected choice here because the statement is only suspected, not asserted as fact.

So for learners, the best model is:

• Hana grunar að lykillinn sé enn í handtöskunni.

That is the form you should learn and use.