"Woolen" isn't a term that you're going to hear much in the United States. We tend to take the material and use it as an adjective almost in the same way the Germans create compound words. Wood is the only material that I can think of that transforms into "wooden" with any consistency.
G - using a Motorola, I get the occasional blip but during the exercise μου was never spoken ( I had to translate Greek spoken phrase into English). It told me I was incorrect and should have had MY at the end of the sentence. At the end of the exercise when "wrong" answer questions are repeated, it clearly missed μου from the audio. I included MY in my answer and was correct. Just an occasional blip I think. Just wondered if others had experienced it. All that being said, love the APP, hopefully Λέχαιο / Άσσος will understand me in June.
From what I listened to, I can hear "μου", but maybe it sounds somewhat muffled and fused with "palto" (paltommm(?)) to a learner. Maybe that's what threw you off. On the other hand, I sometimes get the impression that the audio is less consistent in the web version.
Do we use "το" in this context because we are the coat is the direct object of the sentence?
A two part answer:
- with a possessive, you always need a definite article; "my father" can't simply be πατέρας μου, for example.
- in this sentence, "my wool coat" is the direct object of the sentence, so you need the accusative form of the definite article
Since παλτό is neuter, you need neuter accusative το. (Which happens to look exactly like neuter nominative, since those two cases always look the same for neuter words -- in all Indo-European languages I know of.)