Eftir hringtorgið beygir þú til hægri, og skólinn er þá á vinstri hönd.

Because Icelandic main clauses usually follow a verb-second pattern. Here, the sentence starts with Eftir hringtorgið (after the roundabout), so the finite verb beygir comes next, and the subject þú follows it.

So:

• Eftir hringtorgið beygir þú til hægri = natural word order
• Þú beygir til hægri eftir hringtorgið = also possible, but structured differently

It means after the roundabout or once you have passed the roundabout.

In directions, eftir is often used to locate what happens next in a route. So this phrase tells you that the right turn happens after you reach or pass the roundabout.

Because Icelandic very often makes compound nouns by joining words together.

Here:

• hringur = ring, circle
• torg = square / open space

Together, hringtorg means roundabout. Then -ið is added to mean the, giving hringtorgið = the roundabout.

It is the definite article, attached to the end of the noun. Icelandic usually says the by adding it as a suffix rather than using a separate word.

So:

• hringtorg = a roundabout
• hringtorgið = the roundabout

This is very common in Icelandic:

• skóli = school
• skólinn = the school

Yes. Icelandic often uses the present tense with þú in directions and instructions.

So beygir þú til hægri literally looks like you turn right, but in context it functions like:

• turn right
• you should turn right
• you then turn right

English does something similar in route descriptions: You go straight, then you turn left.

Yes — it is best to learn til hægri as a fixed expression meaning to the right or right in movement/direction.

It is especially common with verbs of turning or movement:

• beygja til hægri = turn right
• fara til hægri = go to the right

So in this sentence, beygir þú til hægri means you turn right.

Þá means then, at that point, or after that.

It links the second part of the directions to the first part:

• first you pass the roundabout
• then you turn right
• then / at that point the school is on your left

So it helps show sequence.

Because the sentence is talking about the school, not just a school.

• skóli = school
• skólinn = the school

In directions, Icelandic often uses the definite form when the place is understood to be a specific landmark.

Literally, it means on the left hand.

But as a normal expression, it means:

• on the left
• on your left-hand side

This is an idiomatic phrase in Icelandic, so it is best to understand it as a chunk: á vinstri hönd = on the left-hand side.

Because the sentence is describing location, not direction of movement.

• til vinstri = to the left / leftward
  Used when someone moves or turns left.
• á vinstri hönd = on the left-hand side
  Used when something is located on your left.

So:

• Beygðu til vinstri = Turn left
• Húsið er á vinstri hönd = The house is on the left

Eventually yes, because Icelandic prepositions often affect the form of the noun that follows them. But for a learner, the most useful approach at first is to learn these as set phrases:

• eftir hringtorgið
• til hægri
• á vinstri hönd

That is often more practical than trying to analyze every ending immediately, especially because some forms are idiomatic or look the same as other cases.

Yes. A more direct command would use the imperative, for example:

• Eftir hringtorgið beygðu til hægri.

That means After the roundabout, turn right.

But the version with beygir þú is also very natural in directions. It sounds like a neutral route description: you turn right.

Because the sentence contains two coordinated main clauses:

• Eftir hringtorgið beygir þú til hægri
• skólinn er þá á vinstri hönd

In Icelandic, it is common to separate this kind of structure with a comma, even before og when both sides are full clauses with their own verbs.