Ég ætti að sofa núna.

In this sentence, ætti gives the idea of should or ought to.

So ég ætti að sofa means something like I should sleep or I ought to sleep.

It is not a simple present-tense form. It is a special form used very often in Icelandic to express:

• advice
• mild obligation
• what would be the sensible thing to do

Yes. Ætti is a form of eiga.

That can be surprising, because eiga often means to own or to have. But Icelandic also uses this verb in very common idiomatic patterns:

• eiga að + infinitive = to be supposed to / to have to
• ætti að + infinitive = should / ought to

So even though the basic verb has another meaning, this pattern is extremely normal and important to learn as a chunk.

This is a very common question.

• Ég á að sofa núna = I am supposed to sleep now / I have to sleep now
• Ég ætti að sofa núna = I should sleep now / I ought to sleep now

A simple way to think about it:

• á að often sounds stronger, more like a rule, plan, duty, or outside expectation
• ætti að is often softer, more like advice, judgment, or what would be best

So ætti að is often less direct than á að.

Because að is the infinitive marker here, like English to.

So:

• sofa = sleep
• að sofa = to sleep

After ætti, Icelandic normally uses að + infinitive:

• ætti að sofa
• ætti að fara
• ætti að lesa

So the structure is very normal.

Because sofa is the infinitive, and the finite verb in the sentence is ætti.

In Ég ætti að sofa núna:

• ég = subject
• ætti = conjugated verb
• að sofa = infinitive phrase

English does something similar:

• I should sleep
• I ought to sleep

The verb after should or ought to is not conjugated either.

Not usually, no.

Even though ætti is historically a past subjunctive form, in modern Icelandic ætti að + infinitive very often refers to a present or future idea:

• what you should do now
• what you ought to do
• what would be advisable

So Ég ætti að sofa núna is naturally understood as a present-time idea, not a past one.

If you want should have, Icelandic often uses hefði átt að + infinitive:

• Ég hefði átt að sofa meira = I should have slept more

Because Icelandic main clauses normally put the finite verb in second position.

Here:

1. Ég comes first
2. ætti comes second

That is exactly what we expect in a normal Icelandic statement.

You can also move another element to the front:

• Núna ætti ég að sofa

That is also correct. But then the verb still stays in second position, and the subject moves after it.

Yes. Both nú and núna mean now.

In many situations they are very close in meaning. A rough guide is:

• nú can sound a bit shorter or more neutral
• núna can sound a bit more conversational, immediate, or emphatic

So both of these are possible:

• Ég ætti að sofa nú
• Ég ætti að sofa núna

For many learners, it is best to just notice that núna is extremely common in everyday speech.

You can do it like this:

• Ég ætti ekki að sofa núna. = I should not be sleeping now / I shouldn't sleep now
• Ætti ég að sofa núna? = Should I sleep now?

Notice that:

• ekki comes after the finite verb
• in a yes/no question, the finite verb ætti comes first

It can depend on context.

English often makes a distinction between:

• I should sleep now
• I should be sleeping now

Icelandic does not always mark that difference the same way, so Ég ætti að sofa núna can cover the general idea of I should be sleeping now.

If you want to be more specific and say I should be asleep now, Icelandic often says:

• Ég ætti að vera sofandi núna.

So:

• að sofa = to sleep
• að vera sofandi = to be asleep / to be sleeping

A rough English-friendly guide is:

• æ sounds like eye
• tt in this kind of word is not a simple English t sound; it is often pronounced with preaspiration, so it can sound a bit like ht

So ætti sounds roughly like eyeh-ti or aih-ti.

A very rough pronunciation of the whole sentence is:

Ég ætti að sofa núna
yeg AIH-ti ah SOH-va NOO-na

That is only an approximation, but it is a useful starting point.