Learn Icelandic: Góðan daginn! Er búðin opin?

In Icelandic, greetings often use the accusative (object) case because they are short for saying 'I wish you a...' So, the basic masculine words góður (good) and dagur (day) change to their accusative forms: góðan and dag.

If the accusative of dagur is dag, where does the -inn in daginn come from?

That is the definite article, which means 'the' in English. In Icelandic, 'the' is attached to the end of the noun instead of being a separate word before it. So dag becomes daginn in the accusative case. You are literally saying 'Good the day!'

How do you form a yes/no question like Er búðin opin?

Just like in English, you swap the subject and the verb to make a question. The statement would be Búðin er opin (The shop is open). To ask a question, you simply put the verb first: Er búðin opin?

Why is the adjective opin (open) spelled with only one 'n' here?

Adjectives in Icelandic have to match the gender of the noun they describe. The word for shop, búð, is a feminine noun. The default dictionary form of 'open' is the masculine opinn, but because it is describing the feminine búðin, it drops an 'n' to become the feminine form opin.