Sjúklingurinn segir að tönnin sé verri á kvöldin.

Yes. The base word is sjúklingur, meaning patient.

The ending -inn is the Icelandic definite article, which is usually attached to the end of the noun rather than written as a separate word. So:

• sjúklingur = a patient
• sjúklingurinn = the patient

Because of the noun’s normal nominative singular ending -ur, the definite form comes out as -urinn.

For the same reason: tönnin is the definite form.

• tönn = a tooth
• tönnin = the tooth

In this sentence, it is a specific tooth that has already been identified from context, so the definite form is natural.

Here að means that and introduces a subordinate clause:

• Sjúklingurinn segir = The patient says
• að tönnin sé verri á kvöldin = that the tooth is worse in the evenings

In English, that is often optional, but in Icelandic að is much more regularly kept.

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

So:

• er = is
• sé = be / is in a subjunctive environment

In sentences like this, Icelandic often uses the subjunctive in a reported statement, especially when the speaker is presenting it as what someone says, thinks, feels, or claims, rather than directly asserting it as a plain fact.

So Sjúklingurinn segir að tönnin sé verri... has the feel of The patient says that the tooth is worse...

If you used er instead, it could sound more like the speaker is treating the content as straightforward fact.

The dictionary forms are:

• segja = to say
• vera = to be

In this sentence:

• segir is 3rd person singular present of segja
• sé is 3rd person singular present subjunctive of vera

So literally:

• sjúklingurinn segir = the patient says
• tönnin sé = the tooth be / is in subjunctive style

Because verri is an adjective form, while verr is usually an adverb.

Here verri describes tönnin, so it must be an adjective agreeing with the noun:

• tönnin er verri = the tooth is worse

But verr is used more like worse in an adverbial sense:

• Mér líður verr = I feel worse

So in this sentence, verri is the correct form because it is saying something about the tooth.

Verri is the comparative form meaning worse.

It is an irregular comparative, so you mostly learn it as a set form rather than building it in a simple predictable way.

The important point here is that Icelandic comparatives can still behave like adjectives and agree with the noun they describe. In this sentence, verri matches tönnin in its grammatical role.

Because tönnin is the subject of the subordinate clause.

In að tönnin sé verri á kvöldin, the structure is basically:

• tönnin = subject
• sé = verb
• verri = predicate adjective

With vera (to be), the subject stays in the nominative, and the adjective agrees with it.

So even though the whole clause comes after að, tönnin is still the subject of that clause.

Because Icelandic very often uses the plural for repeated or habitual times like in the evenings, in the mornings, at nights.

So:

• á kvöldin = in the evenings
• á morgnana = in the mornings

Even if English might use a singular expression, Icelandic often uses this plural definite pattern to talk about something that happens regularly at that time of day.

Á does often mean on, but with time expressions it can be part of fixed idiomatic phrases.

So á kvöldin does not mean something literal like on the evenings in a physical sense. It is just the normal Icelandic way to say in the evenings.

This is one of those expressions that is best learned as a chunk:

• á kvöldin = in the evenings
• á daginn = during the day / in the daytime
• á næturnar = at night / during the nights

Because subordinate clauses in Icelandic normally do not use the main-clause V2 word order.

In the main clause, Icelandic often places the finite verb in second position:

• Sjúklingurinn segir...

But after að, the subordinate clause usually has more regular subject-verb order:

• að tönnin sé verri á kvöldin

So this is the expected word order for a clause introduced by að.