Fyrir aftan húsið eru tvær stórar sorptunnur.

Because Icelandic normally follows a verb-second pattern in main clauses.

Here, the sentence begins with the location phrase Fyrir aftan húsið (behind the house). Once that phrase is put first, the finite verb eru (are) must come next:

• Fyrir aftan húsið = first element
• eru = second element
• tvær stórar sorptunnur = subject

So the structure is very natural in Icelandic, even though it may feel a bit unusual from an English perspective.

Yes, functionally it is. But Icelandic does not need a dummy subject like English there.

English says:

• There are two big trash bins behind the house.

Icelandic simply says:

• Behind the house are two big trash bins.

So eru is just the normal verb to be, and tvær stórar sorptunnur is the real subject.

Fyrir aftan is a fixed expression meaning behind or at the back of.

So:

• fyrir aftan húsið = behind the house

It is best learned as a unit rather than translating each word separately every time.

In this phrase, húsið is used after fyrir aftan, which takes the accusative.

So grammatically, this is:

• hús = house
• húsið = the house
  here, accusative singular definite

One important detail: for many neuter nouns in Icelandic, the nominative and accusative singular look the same. So even though húsið is accusative here, it looks identical to the nominative form.

Because tvær is the form of two used with feminine plural nouns.

The noun sorptunnur is feminine plural, so the numeral must agree with it:

• tveir = two, masculine
• tvær = two, feminine
• tvö = two, neuter

Since sorptunna (trash bin) is feminine, we get:

• tvær sorptunnur = two trash bins

Because adjectives in Icelandic agree with the noun in gender, number, and case.

Here, sorptunnur is:

• feminine
• plural
• nominative (because it is the subject)

So the adjective must match:

• stórar = feminine plural nominative/accusative form of stór (big/large)

That is why we get:

• tvær stórar sorptunnur

and not, for example, stórir or stórt.

Sorptunnur is the nominative plural of sorptunna.

So:

• sorptunna = a trash bin
• sorptunnur = trash bins

In this sentence it is nominative plural because it is the subject of eru.

Also, it is a compound word:

• sorp = trash, rubbish
• tunna = barrel/bin

So sorptunna literally means something like trash bin.

Because the sentence is talking about two big trash bins, not the two big trash bins.

So the noun phrase is indefinite:

• tvær stórar sorptunnur = two big trash bins

If you wanted to make it definite, Icelandic would mark that differently, and the adjective pattern would also change.

Yes. In Icelandic, the subject does not always have to come before the verb.

Here the subject is:

• tvær stórar sorptunnur

You can tell it is the subject because:

• the verb eru is plural and agrees with it
• the noun phrase is in the nominative

So even though it comes after the verb, it is still the subject.

Yes, absolutely.

That version is also correct:

• Tvær stórar sorptunnur eru fyrir aftan húsið.

The difference is mainly one of focus or information structure:

• Fyrir aftan húsið eru tvær stórar sorptunnur.
  starts with the location, so it feels like As for behind the house...
• Tvær stórar sorptunnur eru fyrir aftan húsið.
  starts with the subject, so it feels more straightforward: Two big trash bins are behind the house.

Both are natural.

Because the subject is plural:

• tvær stórar sorptunnur = two big trash bins

The verb vera (to be) agrees with the subject in number, so Icelandic uses:

• er = is
• eru = are

Since there are two bins, the correct form is eru.