Streitan minnkar þegar ég fer í göngutúr.

Because Icelandic usually marks the by attaching it to the end of the noun.
So:

• streita = stress
• streitan = the stress

In a sentence like this, Icelandic often uses the definite form where English might simply say stress.

Streita is a feminine noun. Here, streitan is nominative singular definite because it is the subject of the verb minnkar.

In other words, the stress is the thing that is decreasing.

Minnkar is the present-tense form of the verb minnka, which means to decrease, to lessen, or to get smaller.

Here it is 3rd person singular present, because the subject streitan is grammatically it. So the sentence is literally structured like the stress decreases.

Fara is the infinitive, meaning to go.
Fer is the conjugated present-tense form used with ég.

So:

• að fara = to go
• ég fer = I go / I’m going

You cannot normally use the infinitive fara directly after ég.

Yes. The verb fara is not fully regular in the present tense.

A useful pattern is:

• ég fer
• þú ferð
• hann / hún / það fer
• við förum
• þið farið
• þeir / þær / þau fara

So learners often notice that fer does not look much like the infinitive fara.

Because fara í göngutúr is a very natural Icelandic expression meaning go for a walk or take a walk.

Word-for-word, it is something like:

• fer = go
• í = into / in / on
• göngutúr = walk, walking trip

Even though English often uses walk as the main verb, Icelandic commonly uses fara in this expression.

Here í goes with accusative, because it follows a verb of movement: fara í.

So göngutúr is accusative singular in this sentence.
For this noun, the nominative and accusative singular look the same, so there is no visible spelling change.

Here it means when.

That is because þegar is introducing a clause:

þegar ég fer í göngutúr = when I go for a walk

But þegar can also mean already in other contexts, so this is a very common learner question. In this sentence, the clause structure makes when the correct meaning.

Because þegar introduces a subordinate clause, and subordinate clauses usually have normal subject + verb order.

So:

• þegar ég fer = correct
• þegar fer ég = not the normal order here

Icelandic main clauses often follow the verb-second pattern, but subordinate clauses are different.

Yes. You can say:

Þegar ég fer í göngutúr, minnkar streitan.

That is also correct. But once the þegar clause comes first, the main clause must still follow Icelandic verb-second word order, so you get:

• minnkar streitan
  not
• streitan minnkar

Because Icelandic uses compound nouns very freely.
Göngutúr is a compound noun, roughly built from the idea of walking plus trip/tour.

English sometimes writes similar ideas as separate words, but Icelandic very often joins them into one word.

It can do a bit of both, depending on context. Grammatically, streitan is definite, so it literally means the stress. But Icelandic often uses the definite form for things that are understood from context, even where English might just say stress in a more general way.

So this sentence can still sound natural even if the idea is simply that stress goes down when the speaker goes for a walk.