Learn Hardcore Icelandic: Hún flutti í sveitina í sumar og er mjög ánægð þar. - She moved to the countryside this summer and is very happy there.

Hún flutti í sveitina í sumar – flutti is simple past: she moved (at some point in the past, this summer).
(hún) er mjög ánægð þar – er is present: she is (now) very happy there.

So the structure is:

Past event: the move already happened.
Present state: as a result, she is now happy there.

If you said var mjög ánægð þar, it would suggest she used to be happy there at that past time (this summer), but you say nothing about how she feels now. The original sentence specifically suggests an ongoing present happiness.

What exactly does í sumar mean? Is it in summer, in the summer, or this summer?

Í sumar almost always means this summer (the summer of the current year or the most recent summer, depending on context).

í sumar – usually this summer
í sumarinu – in the summer (more general, with the definite article)
á sumrin – in (the) summers / every summer (habitual)

So your sentence is best understood as:

Hún flutti í sveitina í sumar – She moved to the countryside this summer.

Why is it í sveitina and not í sveitinni or just í sveit?

Three different forms are possible, with different nuances:

í sveitina – accusative + definite article
- Movement into / to a specific countryside area.
- Implies direction: she changed location and went there.
- Literally: into the countryside.
í sveitinni – dative + definite article
- Location in the countryside (no movement).
- You would use this if she is already there and you’re just saying in the countryside:
  - Hún býr í sveitinni – She lives in the countryside.
í sveit – accusative, indefinite (no article)
- Movement into countryside in a more general, non‑specific sense: into countryside / to some rural place.

In your sentence, flutti expresses movement, so í sveitina (accusative of direction) is the natural choice: moved to the countryside.

What does sveit really mean? Is it village, farm, or countryside?

Sveit most often means countryside / rural area, not a specific village or farm:

í sveitina – to the countryside
upp í sveit – up in the countryside (very idiomatic)

Related words:

bær – town, or also a farm (depending on context)
þorp – village
sveitabær – a farm in the countryside

So Hún flutti í sveitina is best understood as She moved to the countryside, not She moved to the village.

Why does ánægð end in -ð, and how does it agree with hún?

Ánægður / ánægð / ánægt is an adjective meaning happy / pleased / satisfied. It agrees in gender and number with the subject:

masculine singular: ánægður
feminine singular: ánægð
neuter singular: ánægt
plural (m/f/n): ánægðir / ánægðar / ánægð

Since hún is feminine singular, the correct form is ánægð:

Hún er mjög ánægð þar. – She is very happy there.
Hann er mjög ánægður þar. – He is very happy there.
Barnið er mjög ánægt þar. – The child is very happy there.

Why is it ánægð þar and not something like ánægð með það?

Both are possible, but they mean slightly different things:

mjög ánægð þar – very happy there
- Focus on her emotional state in that place.
- Implies she likes living/being there.
mjög ánægð með það – very pleased with it
- Focus on satisfaction with some thing / situation / decision, not specifically the location.

In your sentence, we’re talking about how she feels in that place, so ánægð þar is the natural choice.

What is the difference between þar, þarna, and hér, and why is þar used here?

These all translate to there / here, but with slightly different uses:

hér – here (close to the speaker)
þarna – there (over there), relatively specific and often visible or previously pointed out
þar – there in a more abstract, referential way, often to a previously mentioned location

In your sentence:

The place has just been mentioned: í sveitina.
þar refers back to that location:
- … og er mjög ánægð þar. – … and is very happy there (in that place).

Þarna would sound more like physically pointing: there (right there, that spot), which is less natural here.

Is the word order Hún flutti í sveitina í sumar fixed? Could you say Hún flutti í sumar í sveitina?

Both are grammatically possible, but the neutral, most natural order is:

Verb and object/complements,
Then time phrase.

So:

Hún flutti í sveitina í sumar. – very natural
Hún flutti í sumar í sveitina. – possible, but sounds a bit less smooth/neutral, and can put slight emphasis on í sumar.

A common guideline in Icelandic main clauses is:

Subject – Verb – (Object) – Place – Time

Your sentence fits but has time at the end, which is very common and natural in speech:

Hún flutti (S–V) í sveitina (place / direction) í sumar (time).

In English we can say She moved to the countryside this summer without repeating to. Why does Icelandic repeat í in í sveitina í sumar? Can you drop the second í?

In Icelandic, each phrase normally needs its own preposition:

í sveitina – to the countryside
í sumar – this summer

You cannot say *Hún flutti í sveitina sumar; that would be incorrect. The preposition í is required separately for the place phrase and the time phrase. Coordination like in English (to X this summer) without repeating the preposition generally doesn’t work the same way in Icelandic.

So:

Correct: Hún flutti í sveitina í sumar.
Incorrect: *Hún flutti í sveitina sumar.

Why is it í sveitina and not til sveitina? How do í and til differ with places?

Both í and til can express movement, but they’re used differently:

í
- accusative
- movement into / to a place you’ll be in or at
- used with many types of locations:
  - í borgina – to the city
  - í búðina – to the shop
  - í skólann – to school
  - í sveitina – to the countryside
til
- genitive
- movement to(wards) a goal, often a person, town, or country:
  - til Reykjavíkur – to Reykjavík
  - til Íslands – to Iceland
  - til ömmu – to grandma

For sveitina, the natural choice is í because you’re going into / to that area to be there, not just towards it in a more abstract sense.

What is the infinitive of flutti, and how is it conjugated?

The verb is flytja (to move, to transport). Flutti is the past tense, 3rd person singular.

Basic forms:

Infinitive: að flytja – to move
Present 3rd sg.: hún flytur – she moves / is moving
Past 3rd sg.: hún flutti – she moved
Past participle (m./f./n. sg.): fluttur / flutt / flutt – moved

Very rough mini‑paradigm (indicative):

Nútíð (present)
- ég flyt
- þú flytur
- hann/hún/það flytur
- við flytjum
- þið flytjið
- þeir/þær/þau flytja
Þátíð (past)
- ég flutti
- þú fluttir
- hann/hún/það flutti
- við fluttum
- þið fluttuð
- þeir/þær/þau fluttu

What are the gender and case of sveitina, and how is the definite article formed?

Sveitina breaks down like this:

Base noun: sveit – countryside (feminine)
Case: accusative singular (because of movement: í sveitina)
Definite article: -in (feminine singular), which becomes -ina after a consonant cluster / long vowel.

So:

sveit – nominative/accusative, indefinite
sveitin – nominative, definite: the countryside
sveitina – accusative, definite: to the countryside (in context with í)
sveitinni – dative, definite: in the countryside

In your sentence, sveitina is feminine singular accusative definite.