Ég sit á milli gluggans og hurðarinnar.

Yes. Both coordinated nouns must be in the genitive:

• Correct: á milli gluggans og hurðarinnar
• Incorrect: á milli gluggans og hurðinni / á milli gluggans og hurðina

Because the sentence refers to specific, contextually known items (the window and the door in the room). If you meant “a window and a door,” you would use the indefinite genitive forms:

• Definite: gluggans “of the window,” hurðarinnar “of the door”
• Indefinite: glugga “of a window,” hurðar “of a door”

They are the genitive singular with the definite article attached:

• gluggi (window, masc.)
  • Gen. sg. (indef.): glugga
  • • definite article (gen. sg. -ins) → gluggans (glugga + ins → -ans)
• hurð (door, fem.)
  • Gen. sg. (indef.): hurðar
  • • definite article (gen. sg. -innar) → hurðarinnar

Neither. In the fixed preposition á milli, it’s milli that governs the genitive; the á does not assign case. Outside this expression, á by itself takes:

• Dative for location (no motion): Ég sit á stólnum “I’m sitting on the chair.”
• Accusative for motion toward: Ég sest á stólinn “I sit down on the chair.”

sit is the 1st person singular present of sitja “to sit.” Mini present-tense paradigm:

• ég sit
• þú situr
• hann/hún/það situr
• við sitjum
• þið sitjið
• þeir/þær/þau sitja

Use the inchoative verb setjast (“to sit down”), whose 1st person singular present is sest:

• Ég sest á milli gluggans og hurðarinnar. You can add niður for emphasis: Ég sest niður á milli ... (optional).

For “among” (three or more), Icelandic typically uses á meðal or meðal + genitive:

• á meðal vina minna = “among my friends” Use á milli/milli for “between” two items. You will also see expressions like milli þriggja (“between three”), but for general “among,” prefer (á) meðal.

Yes, but the meaning shifts:

• hurð = the door leaf/panel
• dyr (plural-only) = the doorway/entrance So “between the window and the doorway” would be: á milli gluggans og dyranna (note: dyranna is genitive plural definite).