Við tökum stutta pásu og borðum nestið meðan við horfum á útsýnið.

Because the subject is við = we.

In the present tense, Icelandic verbs often take -um in the 1st person plural:

• við tökum = we take
• við borðum = we eat
• við horfum = we look/watch

The dictionary forms are:

• taka = to take
• borða = to eat
• horfa = to look / to watch

So these are just the correctly conjugated present-tense forms for we.

Because pásu is not the basic dictionary form of the noun.

The noun is:

• pása = a break, pause

But after taka in this sentence, it is the direct object, so it appears in the accusative singular:

• pásu

The adjective has to agree with the noun in gender, number, and case, so:

• stuttur = short (dictionary form, masculine)
• stutt / stutta etc. = other inflected forms

So:

• stutta pásu = a short break

Yes. Taka pásu is a very natural way to say take a break in Icelandic.

It works much like English:

• taka pásu = take a break
• taka stutta pásu = take a short break

Another possible expression is gera hlé, which also means take a break / pause, but taka pásu is very everyday and straightforward.

Nesti means food that you bring with you, especially for a trip, hike, journey, or school/work day.

Depending on context, it could be translated as:

• packed lunch
• provisions
• snack you brought along
• food for the trip

So nestið here means the packed food / the lunch we brought with us.

Because Icelandic usually puts the definite article onto the end of the noun instead of using a separate word like English the.

So:

• nesti = packed lunch / provisions
• nestið = the packed lunch / provisions

The ending -ið is the definite article here.

The same thing happens in:

• útsýni = view
• útsýnið = the view

Because Icelandic often leaves out a repeated subject in a coordinated clause when it is clearly the same as before.

So:

• Við tökum stutta pásu og borðum nestið literally has:
• We take a short break and eat the packed lunch

The second við is understood, so it does not need to be repeated.

English does the same thing:

• We take a break and eat not usually
• We take a break and we eat

Because meðan introduces a new clause: while we look at the view.

In that new clause, the subject is normally stated:

• meðan við horfum á útsýnið

So even though the overall subject is still we, the subordinate clause needs its own explicit subject.

That is why:

• og borðum can omit við but
• meðan við horfum normally includes it

Meðan means while.

It introduces a subordinate clause that tells you something is happening at the same time:

• meðan við horfum á útsýnið = while we look at the view

It is a very common word for expressing simultaneous actions.

Because meðan introduces a subordinate clause, and subordinate clauses in Icelandic do not follow the normal main-clause verb-second pattern.

So after meðan, the usual order is:

• meðan við horfum ...
• while we look ...

Compare:

• Main clause: Við horfum á útsýnið.
• Subordinate clause: ... meðan við horfum á útsýnið.

That subject-before-verb order after meðan is normal.

Because horfa á is the normal Icelandic expression for look at or watch.

So:

• horfa á eitthvað = look at something / watch something

The á is part of the verb expression here, not just a literal on.

Examples:

• horfa á sjónvarp = watch television
• horfa á fuglana = look at the birds
• horfa á útsýnið = look at the view

So you should learn horfa á as a unit.

Syntactically, it is the object of horfa á, so it is accusative.

However, útsýni is a neuter noun, and in the singular definite form, the nominative and accusative look the same:

• útsýnið

So in this sentence it is functioning as accusative, even though the form is identical to nominative.

Yes.

Icelandic present tense can describe:

• something happening now
• something that usually happens
• sometimes even a planned or vivid action in context

So this sentence could mean:

• We take a short break and eat our packed lunch while looking at the view as a description of what is happening now, or
• a typical thing we do on a trip

The exact feel depends on context.