Þokan er svo þykk að við keyrum hægt.

Þokan means the fog, while þoka means simply fog.

Icelandic usually adds the definite article to the end of the noun instead of using a separate word like English the.

• þoka = fog
• þokan = the fog

So Þokan er svo þykk... means The fog is so thick...

The adjective þykk has to agree with the noun it describes.

Here, þokan is:

• feminine
• singular
• nominative (because it is the subject of the sentence)

So the adjective also takes the feminine singular nominative form:

• masculine: þykkur
• feminine: þykk
• neuter: þykkt

That is why we get þokan er svo þykk.

Svo ... að means so ... that.

It is a very common Icelandic pattern used to show result:

• Hann er svo þreyttur að hann sofnar strax. = He is so tired that he falls asleep immediately.
• Þokan er svo þykk að við keyrum hægt. = The fog is so thick that we drive slowly.

So:

• svo = so
• að = that

Here að is a conjunction meaning that. It connects the first clause to the result clause.

So the sentence is divided like this:

• Þokan er svo þykk = The fog is so thick
• að við keyrum hægt = that we drive slowly

Do not confuse this að with the infinitive marker, which can also mean to before a verb.

Because keyrum is the correct present-tense form for we drive.

The verb is að keyra = to drive.
In the present tense:

• ég keyri = I drive
• þú keyrir = you drive
• hann/hún/það keyrir = he/she/it drives
• við keyrum = we drive
• þið keyrið = you all drive
• þeir/þær/þau keyra = they drive

So after við you need keyrum, not the infinitive keyra.

In Icelandic, adjectives are often used in the neuter singular form as adverbs.

So:

• hægur / hæg / hægt = slow
• keyra hægt = drive slowly

This is very common in Icelandic. English usually uses -ly, but Icelandic often uses the neuter adjective form instead.

Other examples:

• hann talar hátt = he speaks loudly
• hún syngur fallega is also possible with a true adverbial form, but many common adverb-like uses come from adjective forms
• við göngum hratt = we walk quickly

So hægt literally comes from the adjective, but here it functions like an adverb.

Yes. Er is the present tense form of að vera = to be.

In this sentence, þokan er svo þykk means the fog is so thick.

A few present-tense forms of vera are:

• ég er = I am
• þú ert = you are
• hann/hún/það er = he/she/it is
• við erum = we are

So er is simply is here.

No. After að meaning that, Icelandic normally keeps the usual clause order:

• við keyrum hægt = we drive slowly

So:

• Þokan er svo þykk að við keyrum hægt.

This is normal subordinate-clause order in Icelandic for this kind of sentence.

Verb-first order happens in some other structures, especially yes/no questions:

• Keyrum við hægt? = Are we driving slowly?

But not here.

These two letters are very important in Icelandic:

• þ is like th in thing
• ð is like th in this

In your sentence:

• Þokan starts with þ, so the first sound is like th in thin
• að contains ð, so it sounds like the th in that
• við also contains ð

So roughly:

• Þokan ≈ THO-kan
• að ≈ ath / adh
• við ≈ vith / vidh

The exact Icelandic pronunciation is a bit different from English, but that is the closest guide.

Þokan is in the nominative case because it is the subject of the sentence.

The basic idea:

• the thing that is something, or does something, is usually nominative

Here, the fog is the subject of er:

• Þokan er svo þykk = The fog is so thick

So:

• nominative singular indefinite: þoka
• nominative singular definite: þokan

Yes, depending on context, við keyrum hægt can often be understood as either:

• we drive slowly
• we are driving slowly

Icelandic present tense often covers both simple present and present progressive, where English makes a distinction.

So the sentence can describe:

• a general situation: We drive slowly when the fog is thick
• a current situation: We are driving slowly because the fog is thick

The surrounding context tells you which is meant.

Yes. Svo is a very common word in Icelandic and can have several meanings depending on context, such as:

• so
• then
• thus
• sometimes part of fixed expressions

In this sentence, though, the meaning is clearly so in the pattern svo ... að = so ... that.

So here you should read:

• svo þykk = so thick