Ég tók strax eftir því að hún var óviss þegar hún svaraði spurningunni.

Yes. Taka eftir is a very common Icelandic expression meaning to notice or to pay attention to.

So in this sentence:

• tók = past tense of taka = take
• eftir by itself often means after
• but taka eftir together does not mean take after here

It functions as a set expression:

• taka eftir einhverju/einhverjum = notice something/someone

So Ég tók strax eftir... means I noticed right away...

Because taka eftir normally takes a dative object, and when the thing you notice is a whole clause, Icelandic usually uses the pattern:

taka eftir því að + clause

Here:

• því is the dative form of það
• að hún var óviss is the clause explaining what was noticed

So the structure is roughly:

• Ég tók eftir því = I noticed it
• að hún var óviss = that she was uncertain

Put together:

• Ég tók eftir því að... = I noticed that...

For learners, this is best treated as a standard pattern you should memorize.

In very casual speech, you may sometimes hear variation, but standard Icelandic strongly prefers:

taka eftir því að...

So as a learner, the safest and most natural choice is to keep því.

A good rule:

• with a noun/pronoun object: taka eftir henni, taka eftir hljóðinu
• with a full that-clause: taka eftir því að...

Because this is a subordinate clause introduced by að.

In Icelandic, main clauses usually follow the V2 rule, where the finite verb is in the second position. But subordinate clauses introduced by words like að and þegar do not follow that same main-clause pattern.

So you get:

• main clause: Ég tók strax eftir því...
• subordinate clause: að hún var óviss
• subordinate clause: þegar hún svaraði spurningunni

In both subordinate clauses, the subject comes before the verb:

• hún var
• hún svaraði

Good question. Óviss is an adjective, and it does agree with hún. But in this adjective, the masculine and feminine nominative singular forms are the same.

So:

• masculine: óviss
• feminine: óviss
• neuter: óvisst

That means hún var óviss is completely correct. Even though the subject is feminine, the form still appears as óviss.

Because this sentence is stating something as a simple fact in the past.

The speaker is describing what they noticed:

• she was uncertain
• she answered the question

So the normal past indicative is used:

• var = was
• svaraði = answered

There is no special hypothetical or doubtful meaning here that would require a different mood.

Strax means right away, immediately, or at once.

So:

• Ég tók strax eftir því... = I noticed right away...

It tells you the speaker noticed her uncertainty very quickly.

Its placement here is very natural:

• Ég tók strax eftir því...

You can think of it as modifying the whole noticing action.

Because the verb svara takes the dative case in Icelandic.

So Icelandic says:

• svara einhverju = answer something

The noun spurning means question, and here it appears in the dative singular definite form:

• spurning = question
• spurningu = a question / to a question (dative singular indefinite)
• spurningunni = the question (dative singular definite)

So:

• hún svaraði spurningunni = she answered the question

This is something you have to learn with the verb:

• svara + dative

It shows two things at once:

1. dative singular
2. definite article = the

In Icelandic, the definite article is usually attached to the end of the noun instead of being a separate word.

So:

• spurning = question
• spurningin = the question (nominative)
• spurningunni = the question (dative)

This is very typical of Icelandic noun forms.

Here þegar is a time conjunction meaning when. In context, it can also feel a bit like as or while.

So:

• þegar hún svaraði spurningunni = when she answered the question
• or more naturally in context, as she was answering the question

It tells you when the speaker noticed her uncertainty.

Because there are two separate subordinate clauses, and each one has its own subject.

The sentence contains:

• að hún var óviss
• þegar hún svaraði spurningunni

In both clauses, hún is the subject:

• she was uncertain
• she answered the question

English would also usually repeat she here, so this is very natural.

There are three especially useful ones:

• taka → tók
  strong verb, past tense: take → took

• vera → var
  very common irregular verb: be → was

• svara → svaraði
  weak verb: answer → answered

So this sentence is also a nice example of different verb types:

• a strong verb: tók
• an irregular very common verb: var
• a regular weak verb: svaraði

A useful way to break it down is:

Ég tók strax eftir því
main clause

að hún var óviss
content clause: what I noticed

þegar hún svaraði spurningunni
time clause: when this was happening

So the full structure is:

• I noticed right away
• that she was uncertain
• when/as she answered the question

This kind of layering is very common in Icelandic, and recognizing the clause boundaries makes the sentence much easier to understand.