Ég fer sjaldan í bíó á virkum dögum.

Fer is the 1st person singular present tense form of the verb fara (to go).

So:

• að fara = to go
• ég fer = I go
• þú ferð = you go
• hann/hún/það fer = he/she/it goes

In Icelandic, you usually do not use the infinitive after the subject the way dictionary forms are listed. You need the conjugated form, so Ég fer = I go.

Here it means I go in the sense of a habit or general pattern.

Because the sentence also has sjaldan (seldom / rarely), the whole sentence is understood as something habitual:

• Ég fer sjaldan í bíó á virkum dögum.
• I rarely go to the cinema on weekdays.

Icelandic often uses the simple present for habitual actions, just like English does here.

Sjaldan means seldom, rarely.

Its position here is very natural in Icelandic:

• Ég fer sjaldan ...
• literally: I go rarely ...

A common basic Icelandic word order is:

• subject + verb + adverb + rest

So this sentence is very normal and neutral.

You can also move sjaldan for emphasis in some contexts, for example:

• Sjaldan fer ég í bíó á virkum dögum.

That sounds more marked or emphatic, something like Rarely do I go to the cinema on weekdays.

Fara í bíó is a very common Icelandic expression meaning to go to the cinema / to go see a movie.

Even though í often literally means in/into, this phrase is idiomatic and standard. Icelandic commonly uses:

• fara í skólann = go to school
• fara í vinnuna = go to work
• fara í bíó = go to the cinema

So for a learner, it is best to remember í bíó as a set phrase.

Because bíó in this expression works almost like a fixed activity/place expression: go to the cinema.

In Icelandic, you often do not need a separate word for the, because definiteness is usually expressed differently than in English, often with a suffixed article. But in í bíó, the phrase is just used without an article.

So:

• í bíó = to the cinema / to the movies

This is simply the normal way to say it.

Here í takes the accusative, because it expresses movement toward/into something.

A very important Icelandic pattern is:

• í + accusative for motion/direction
• í + dative for location

Compare:

• Ég fer í bíó. = I go to the cinema.
  (movement → accusative)

• Ég er í bíói. = I am in the cinema.
  (location → dative)

So in your sentence, fara involves motion, so í goes with the accusative.

Á virkum dögum means on weekdays.

This is a time expression, and with á in this kind of usage, Icelandic uses the dative plural here.

Breaking it down:

• virkur = active / working
• dagur = day

In the phrase:

• virkum = dative plural of virkur
• dögum = dative plural of dagur

So literally it is something like:

• on working days

which naturally means on weekdays.

Because Icelandic adjectives must agree with the nouns they describe.

That means the adjective changes to match the noun in:

• gender
• number
• case

Here:

• dögum is plural
• it is in the dative
• dagur is masculine

So the adjective virkur must match that form:

• virkum dögum

This kind of agreement is a major feature of Icelandic grammar.

Yes. A very common contrast is:

• á virkum dögum = on weekdays
• um helgar = on weekends

These are both standard time expressions, but they use different prepositions because Icelandic idiom simply works that way. So it is best to learn them as chunks.

For example:

• Ég vinn á virkum dögum. = I work on weekdays.
• Ég fer oft í bíó um helgar. = I often go to the cinema on weekends.

The given order is the most neutral and natural one:

• Ég fer sjaldan í bíó á virkum dögum.

But Icelandic does allow some flexibility for emphasis.

For example:

• Sjaldan fer ég í bíó á virkum dögum.

This emphasizes sjaldan more strongly.

However, Icelandic is still a verb-second language in main clauses, so when something other than the subject comes first, the finite verb usually stays in second position:

• Sjaldan fer ég ... not
• Sjaldan ég fer ...

So yes, there is some flexibility, but not complete freedom.

Yes, it sounds very natural.

It uses several very common Icelandic patterns:

• Ég fer = present tense of fara
• sjaldan in a normal adverb position
• fara í bíó as a standard expression
• á virkum dögum as a natural time phrase

So this is exactly the kind of sentence a native speaker might say in everyday conversation.

Yes. In natural English translation, í bíó can correspond to:

• to the cinema
• to the movies
• sometimes even to see a movie

depending on context.

So in this sentence, all of these are reasonable English equivalents:

• I rarely go to the cinema on weekdays.
• I rarely go to the movies on weekdays.

The Icelandic phrase itself is very standard and broad in that way.