"There is a dog under the window."
Translation:Под окном собака.
With the most common stress (on the last words) that would rather be "The dog is under the window". Russian tend to say "definite" things first.
You can say "Собака под окном" making a stress on "собака". This way, it will answer the question "Who is under the window?" and sound like talking with a toddler: Кто под окном? Собака под окном! Who is under the window? A dog is under the window!
Window is in the instrumental case? So why in another exercise it was над дверую, which looks like prepositional to me?
"Дверью" is Instrumental. The Prepositional case would be "двери". "Двери" it's also the Genitive and the Dative but that's incidental.
So -ом, -ой et -у are the singular endings of the instrumental case. I didn't know the last one.
No, not -у, only -ю. It's the ending of the Instrumental case of the feminine nouns ending in -ь. "Мышь" - "мышью" ("mouse"), "боль" - "болью" ("pain"), "кровать" - "кроватью" ("bed"), "власть" - "властью" ("power").